Jeffrey Lagarias

Q: What Schools Are Affiliated With Jeffrey Lagarias

Jeffrey Lagarias is affiliated with the following schools: University of Michigan, Massachusetts Institute of Technology, University of Illinois Urbana-Champaign

Jeffrey Lagarias's AcademicInfluence.com Rankings

Jeffrey Lagarias

Mathematics

#1260

World Rank

#2106

Historical Rank

#526

USA Rank

Measure Theory

#943

World Rank

#1228

Historical Rank

#351

USA Rank

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Mathematics

Why Is Jeffrey Lagarias Influential?

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According to Wikipedia, Jeffrey Clark Lagarias is a mathematician and professor at the University of Michigan. Education While in high school in 1966, Lagarias studied astronomy at the Summer Science Program. He completed an S.B. and S.M. in Mathematics at the Massachusetts Institute of Technology in 1972. The title of his thesis was "Evaluation of certain character sums". He was a Putnam Fellow at MIT in 1970. He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of the class group of a quadratic field", in 1974. His advisor for both his masters and Ph.D was Harold Stark.

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Jeffrey Lagarias's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The 3x + 1 Problem and its Generalizations (1985) (510)
Two-scale difference equations II. local regularity, infinite products of matrices and fractals (1992) (504)
Solving low density subset sum problems (1983) (501)
Two-scale difference equations I: existence and global regularity of solutions (1991) (428)
Sets of Matrices All Infinite Products of Which Converge (1992) (403)
Tiling with polyominoes and combinatorial group theory (1990) (237)
The computational complexity of knot and link problems (1997) (231)
Self-affine tiles in ℝn (1996) (221)
The finiteness conjecture for the generalized spectral radius of a set of matrices (1995) (207)
The Ultimate Challenge: The 3x+1 Problem (2011) (194)
Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice (1991) (187)
A bound for the least prime ideal in the Chebotarev Density Theorem (1979) (178)
Integral self-affine tiles in ℝn I. Standard and nonstandard digit sets (1996) (176)
An Elementary Problem Equivalent to the Riemann Hypothesis (2000) (171)
Tiling the line with translates of one tile (1996) (170)
Apollonian circle packings:number theory (2000) (152)
Geometric Models for Quasicrystals I. Delone Sets of Finite Type (1999) (148)
Euler's constant: Euler's work and modern developments (2013) (145)
Complements to Li's Criterion for the Riemann Hypothesis☆ (1999) (137)
The 3x+1 problem: An annotated bibliography (2003) (136)
Beyond the Descartes Circle Theorem (2001) (134)
Polynomial Time Algorithms for Finding Integer Relations Among Real Numbers (1989) (133)
Meyer's concept of quasicrystal and quasiregular sets (1996) (132)
Reconstructing Truncated Integer Variables Satisfying Linear Congruences (1988) (119)
Keller’s cube-tiling conjecture is false in high dimensions (1992) (117)
The number of Reidemeister moves needed for unknotting (1998) (98)
Spectral Sets and Factorizations of Finite Abelian Groups (1997) (96)
Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group (2000) (95)
Orthonormal bases of exponentials for the n-cube (2000) (94)
Integral self-affine tiles in ℝn part II: Lattice tilings (1997) (93)
Structure of tilings of the line by a function (1996) (88)
Worst-Case Complexity Bounds for Algorithms in the Theory of Integral Quadratic Forms (1980) (86)
Corrigendum/addendum to: Sets of matrices all infinite products of which converge (2001) (84)
Geodesic Multidimensional Continued Fractions (1994) (77)
Best simultaneous Diophantine approximations. I. Growth rates of best approximation denominators (1982) (72)
Sets uniquely determined by projections on axes II Discrete case (1991) (72)
Haar Type Orthonormal Wavelet Bases in R2 (1995) (70)
The zeta function of the beta transformation (1994) (70)
Computing n(X) the meissel-lehmer method (1985) (70)
The Takagi function and its properties (2011) (69)
On the range of fractional parts {ξ(p/q)ⁿ} (1995) (65)
The quality of the Diophantine approximations found by the Jacobi-Perron algorithm and related algorithms (1993) (63)
The 3x+1 Problem: An Annotated Bibliography, II (2000-2009) (2006) (63)
The 3x+1 problem: An annotated bibliography (1963--1999) (2003) (62)
Substitution Delone Sets (2001) (59)
Apollonian Circle Packings : Geometry and Group Theory (2005) (59)
On the computational complexity of determining the solvability or unsolvability of the equation ²-²=-1 (1980) (57)
The set of rational cycles for the 3x+1 problem (1990) (55)
The set of primes dividing the Lucas numbers has density 2∕3 (1985) (55)
Knapsack Public Key Cryptosystems and Diophantine Approximation (1983) (54)
Multiregular Point Systems (1998) (53)
Best simultaneous Diophantine approximations. II. Behavior of consecutive best approximations (1982) (53)
THE 3x + 1 PROBLEM: TWO STOCHASTIC MODELS (1992) (52)
ON THE THERMODYNAMIC FORMALISM FOR MULTIFRACTAL FUNCTIONS (1994) (52)
The Riemann hypothesis for certain integrals of Eisenstein series (解析的整数論とその周辺研究集会報告集) (2004) (52)
Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings (2000) (51)
Sets Uniquely Determined by Projections on Axes I (1990) (49)
The Kepler conjecture : the Hales-Ferguson proof by Thomas Hales, Samuel Ferguson (2011) (45)
Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions (2000) (45)
Li coefficients for automorphic $L$-functions (2004) (44)
Geometric Models for Quasicrystals II. Local Rules Under Isometries (1999) (44)
Point lattices (1996) (42)
A walk along the branches of the extended Farey Tree (1995) (41)
Mysteries in packing regular tetrahedra (2012) (40)
On the robustness of single-loop sigma-Delta modulation (2001) (40)
Cryptology and Computational Number Theory (1997) (40)
Computing pi(x): An Analytic Method (1987) (39)
On computing artin l-functions in the critical strip (1979) (38)
Haar Bases for L 2 (R n ) and Algebraic Number Theory (1996) (38)
Benford's Law for the 3x + 1 Function (2005) (38)
Hilbert Spaces of Entire Functions and Dirichlet L-Functions (2006) (38)
Local Complexity of Delone Sets and Crystallinity (2001) (38)
On a positivity property of the Riemann ξ-function (1999) (36)
One-Way Functions and Circuit Complexity (1986) (36)
Bounds for the 3x+1 problem using difference inequalities (2002) (36)
Self-Affine Tiles in (1994) (35)
The lap-counting function for linear mod one transformations I: explicit formulas and renormalizability (1996) (34)
On the existence of fields governing the 2-invariants of the classgroup of (√) as varies (1983) (32)
Linear Congruential Generators Do Not Produce Random Sequences (1984) (31)
Ternary expansions of powers of 2 (2005) (31)
Haar Bases forL2(Rn) and Algebraic Number Theory (1996) (29)
Karmarkar's linear programming algorithm and Newton's method (1991) (29)
The Schr\"odinger operator with Morse potential on the right half line (2007) (29)
Zero Spacing Distributions for Differenced L-Functions (2006) (29)
Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups (2000) (28)
The Takagi function and its properties (Functions in Number Theory and Their Probabilistic Aspects) (2012) (26)
EXISTENCE AND GLOBAL REGULARITY OF SOLUTIONS * (26)
On a two-variable zeta function for number fields (2001) (26)
The 3x+1 Problem: An Overview (2021) (26)
The Lerch zeta function I. Zeta integrals (2010) (25)
On the distribution in short intervals of integers having no large prime factor (1987) (25)
Stochastic Models for the 3x+1 and 5x+1 Problems (2009) (24)
The Lerch zeta function II. Analytic continuation (2010) (23)
Bounds for Local Density of Sphere Packings and the Kepler Conjecture (2000) (23)
BEST SIMULTANEOUS DIOPHANTINE APPROXIMATIONS (2004) (23)
Performance Analysis of Shamir's Attack on the Basic Merkle-Hellman Knapsack Cryptosystem (1984) (22)
Monotonicity properties of the Toda flow, the QR-Flow, and subspace iteration (1991) (22)
A Polyomino Tiling Problem of Thurston and Its Configurational Entropy (1993) (21)
Lower bounds for the total stopping time of 3x + 1 iterates (2001) (20)
On the Density of Sequences of Integers the Sum of No Two of which Is a Square. I. Arithmetic Progressions (1982) (20)
Asymmetric Tent Map Expansions. I. Eventually Periodic Points (1993) (20)
Succinct certificates for the solvability of binary quadratic Diophantine equations (1979) (20)
Single-suit two-person card play (1987) (20)
Orthogonality criteria for compactly supported refinable functions and refinable function vectors (2000) (20)
Singularities of Minimal Surfaces and Networks and Related Extremal Problems in Minkowski Space (1990) (20)
Linear fractional transformations of continued fractions with bounded partial quotients (1997) (19)
Density bounds for the 3x + 1 problem. II: Krasikov inequalities (1995) (19)
Level sets of the Takagi function: local level sets (2010) (18)
On the Capacity of Disjointly Shared Networks (1985) (18)
Sets of primes determined by systems of polynomial congruences (1983) (18)
On the Density of Sequences of Integers the Sum of No Two of Which Is a Square II. General Sequences (1983) (18)
Density bounds for the 3x + 1 problem. I: tree-search method (1995) (18)
Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles (2003) (18)
On the Normality of Arithmetical Constants (2001) (18)
Algorithms for Packing Squares: A Probabilistic Analysis (1989) (17)
The Distribution of 3x+1 Trees (1995) (17)
Apollonian circle packings: Number theory II. Spherical and hyperbolic packings (2004) (17)
Level sets of the Takagi function: Generic level sets (2010) (16)
Threading Homotopies and DC Operating Points of Nonlinear Circuits (1998) (16)
Unique Extrapolation of Polynomial Recurrences (1988) (16)
Best Diophantine approximations to a set of linear forms (1983) (16)
Multivariate descartes rule of signs and sturmfels’s challenge problem (1997) (16)
Probabilities for intersecting systems and random subsets of finite sets (1986) (15)
Optimal pairs of score vectors for positional scoring rules (1982) (15)
Cutting Sequences for Geodesic Flow on the Modular Surface and Continued Fractions (1997) (15)
Configuration spaces of equal spheres touching a given sphere: The twelve spheres problem (2016) (14)
The Lerch Zeta function III. Polylogarithms and special values (2015) (14)
Cube-tilings of ℝn and nonlinear codesand nonlinear codes (1994) (14)
Smooth solutions to the abc equation: the xyz Conjecture (2009) (14)
The lap-counting function for linear mod one transformations II: the Markov chain for generalized lap numbers (1997) (14)
Bounds for the number of DC operating points of transistor circuits (1999) (14)
Polyharmonic Maass forms for PSL(2,Z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {PSL}(2,{\mathbb Z})$$\end{ (2015) (14)
Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra (2005) (13)
Asymmetric tent map expansions II. Purely periodic points (1994) (13)
Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers (2003) (13)
Cube-Tilings of Rn and Nonlinear Codes (1994) (13)
Guest Editors' Foreword (2006) (13)
On determining the 4-rank of the ideal class group of a quadratic field (1980) (12)
Well-Spaced Labelings of Points in Rectangular Grids (2000) (11)
Corrigendum and Addendum to: Haar Bases for L^2(R^n) and Algebraic Number Theory (1998) (11)
On the Tightest Packing of Sums of Vectors (1983) (11)
Multi-Stage Planning and the Extended Linear-Quadratic-Gaussian Control Problem (1983) (10)
Area Inequalities for Embedded Disks Spanning Unknotted Curves (2003) (10)
The Kepler Conjecture and Its Proof (2011) (10)
The lap-counting function for linear mod one transformations III: the period of a Markov chain (1997) (10)
The 3x + 1 semigroup (2004) (10)
Polytopes that Fill Rn and Scissors Congruence (1995) (9)
Single-Suit Two-Person Card Play III. The Misère Game (1989) (9)
Evaluation of the Adleman Attack on Multiply Iterated Knapsack Cryptosystems (1983) (9)
The impact of aperiodic order on mathematics (2000) (9)
Minimum range sequences of all k-subsets of a set (1977) (9)
New algorithms for computing π(x) (1984) (9)
Simultaneously good bases of a lattice and its reciprocal lattice (1990) (9)
Polynomial Splitting Measures and Cohomology of the Pure Braid Group (2016) (9)
p-adic path set fractals and arithmetic (2012) (9)
Signatures of units and congruences (mod 4) in certain real quadratic fields. II. (1980) (8)
The Kruskal Count (2001) (8)
Approximate Squaring (2003) (8)
The Kepler Conjecture (2011) (8)
Errata to: “The set of primes dividing the Lucas numbers has density 2∕3” (1994) (8)
Dilated Floor Functions That Commute (2016) (7)
Polyharmonic Maass forms for $$\text {PSL}(2,{\mathbb Z})$$PSL(2,Z) (2016) (7)
Beurling generalized integers with the Delone Property (1999) (7)
Counting dyadic equipartitions of the unit square (2002) (7)
A Skolem–Mahler–Lech Theorem for Iterated Automorphisms of K–algebras (2013) (7)
The Integral of the Riemann xi-function (2011) (7)
The EKG Sequence (2002) (7)
Simultaneous Diophantine approximation of rationals by rationals (1986) (7)
The twelve spheres problem (2016) (7)
The d-Step Conjecture and Gaussian Elimination (1997) (7)
Signatures of units and congruences (mod 4) in certain totally real fields. (1980) (6)
Polytopes that fill ℝn and scissors congruenceand scissors congruence (1995) (6)
Path sets in one-sided symbolic dynamics (2012) (6)
The lap-counting and zeta functions of the tent map (2000) (6)
Single-suit two-person card play II. Dominance (1988) (6)
Splitting behavior of Sn-polynomials (2014) (6)
Products of binomial coefficients and unreduced Farey fractions (2014) (6)
Nonnegative radix representations for the orthant R(+)(n) (1996) (5)
Counting d -Step Paths in Extremal Dantzig Figures (1998) (5)
Shifted polyharmonic Maass forms for ${\rm PSL} (2,{\mathbb Z})$ (2017) (5)
The Riemann Hypothesis : Arithmetic and Geometry (2006) (5)
The Lerch zeta function IV. Hecke operators (2015) (5)
Products of Farey Fractions (2015) (5)
The continuous Diophantine approximation mapping of Szekeres (1995) (5)
A family of measures on symmetric groups and the field with one element (2015) (5)
Number Theory and Dynamical Systems (Preliminary Notes) (1991) (5)
Processor Shadowing: Maximizing Expected Throughput in Fault-Tolerant Systems (1999) (5)
Acknowledgment of priority concerning: Polytopes that Fill ℝn and scissors congruence (1995) (5)
Product-free sets with high density (2011) (4)
The 3 x + 1 Problem : An Annotated Bibliography ( 1963 – 2000 ) (2006) (4)
The Minimal Number of Triangles Needed to Span a Polygon Embedded in ℝd (2003) (4)
Problems: 10585-10591 (1997) (4)
Signatures of units and congruences (mod 4) in certain real quadratic fields. (1978) (4)
The Wild Numbers (2004) (4)
HIGHER CORRELATIONS AND THE ALTERNATIVE HYPOTHESIS (2019) (4)
Intersections of Multiplicative Translates of 3-Adic Cantor Sets II: Two Infinite Families (2013) (4)
Bounds for the number of DC operating points of transistor networks (1997) (3)
Erratum to: Errata The Kepler Conjecture: The Hales-Ferguson Proof (2012) (3)
Effects of misspecification of lag structure in certain two-variable distributed lag models (1991) (3)
Wild and Wooley Numbers (2004) (3)
Moser's Shadow Problem (2013) (3)
Correction to: ``On a positivity property of the Riemann ξ-function'' (Acta Arith. 89 (1999), 217–234) (2005) (3)
Cyclic systems of simultaneous congruences (2007) (3)
The Maximal Density of Product-Free Sets in ℤ/nℤ (2011) (2)
ERGODICITY OF THE ACTION OF K∗ ON AK (2013) (2)
Path Sets and their Symbolic Dynamics (2012) (2)
Solid Angles of a Tetrahedron: 10598 (1999) (2)
Interference-Minimizing Colorings of Regular Graphs (1998) (2)
A Course in Number Theory and Cryptography (Neil Koblitz) (1989) (2)
Problems: 10494-10500 (1996) (2)
CORRIGENDUMADDENDUM Haar Bases for L 2 (R n ) and Algebraic Number Theory (1999) (2)
The Lerch zeta function and the Heisenberg group (2015) (2)
A complement to Rident's P-adic generalization of the Thue-Siegel-Roth theorem (1981) (2)
p-adic path set fractals (2012) (1)
Notes on Cardinal's Matrices (2015) (1)
Partial factorizations of products of binomial coefficients (2020) (1)
Succinct certificates for solutions to binary quadratic Diophantine equations (2006) (1)
DIVISIBILITY PROPERTIES OF SOME CYCLOTOMIC SEQUENCES (1980) (1)
Random Hill’s Equations, Random Walks, and Products of Random Matrices (2013) (1)
Correction to : “Linear fractional transformations of continued fractions with bounded partial quotients” (2003) (1)
Interleaving of path sets (2021) (1)
Delone set models for quasicrystals (2003) (1)
Problems: 10346-10353 (1993) (1)
Conway’s Work on Iteration In memory of John Horton Conway (1937–2020) (2021) (1)
Very Composite Numbers: 11334 [2008, 71] (2009) (1)
DENSITY BOUNDS FOR THE 3 x + 1 PROBLEM . II (2010) (1)
Elementary Problems: E2873-E2877 (1981) (1)
Beyond the Descartes circle theorem (American Mathematical Monthly (2002) 109, 338-361)) (2008) (1)
On Lasker's card game (1989) (1)
Large Values of Tangent: 10656 (1999) (1)
Baking a Pi with Factorials: 11333 [2007, 926]. (2009) (1)
Dilated floor functions having nonnegative commutator I. Positive and mixed sign dilations (2018) (1)
Ergodicity of the Action of K* on (2012) (1)
Erdős, Klarner, and the 3x + 1 Problem (2016) (1)
Level sets of the Takagi function: local level sets (2012) (1)
On the space requirements of navigational relationship representations (1981) (1)
N T ] 1 7 O ct 2 00 3 Apollonian Circle Packings : Number Theory (2003) (1)
Band-limited mimicry of point processes by point processes supported on a lattice (2019) (1)
The Parameter Space of the d-step Conjecture (1996) (1)
Apollonian Circle Packings : Number (2000) (1)
2 2 A pr 2 00 8 The 3 x + 1 Problem : An Annotated Bibliography , II ( 2001 – ) (2009) (1)
N T / 0 00 91 13 v 2 1 7 O ct 2 00 3 Apollonian Circle Packings : Number Theory (2005) (0)
Problems: 10550-10556 (1996) (0)
Multiregular Point Systems Multiregular Point Systems (1997) (0)
The Takagi Function and Related Functions (2010) (0)
Splitting behavior of Sn-polynomials (2015) (0)
1 1 Ju l 2 00 8 Ternary Expansions of Powers of 2 (2008) (0)
A lie bracket decomposition and its application to flows on symmetric matrices (1992) (0)
A Dynamical Systems Construction of a Counterexample to the Finiteness Conjecture (2005) (0)
AREA INEQUALITIES FOR EMBEDDED DISKS SPANNING (2006) (0)
N T ] 2 0 A pr 2 00 4 Comment on : Absolute Derivations and Zeta Functions (2004) (0)
Problems in number theory related to aperiodic order (2021) (0)
Dilated floor functions having nonnegative commutator II. Negative dilations (2019) (0)
Book Review: Dense sphere packings: a blueprint for formal proofs (2015) (0)
Ja n 20 03 Dynamics of a Family of Piecewise-Linear Area-Preserving Plane Maps I . Invariant Circles (2003) (0)
When Periodic Points Are Real: 10822 (2001) (0)
A pr 2 00 0 Repetitive Delone Sets and Quasicrystals (2000) (0)
Eighteen Hundred Years to a Corrigendum (2012) (0)
Rationals to and Only to Rationals: 10555 (1998) (0)
Problems: 10473-10479 (1995) (0)
The Geometry and Combinatorics of Ehrhart δ-Vectors (2009) (0)
Decimation and interleaving operations in one-sided symbolic dynamics (2020) (0)
2 1 A pr 2 00 4 Li Coefficients for Automorphic L-Functions (2004) (0)
Advanced Problems: 6661-6663 (1991) (0)
A Note on Absolute Derivations and Zeta Functions (2004) (0)
Affine Isoperimetric Inequalities for Piecewise Linear Surfaces (2002) (0)
The EKG Sequence: 10927 (2004) (0)
A Generous Bound for Divisor Sums: 10949 (2004) (0)
The Lerch Zeta function III. Polylogarithms and special values (2016) (0)
Decay of a Markov Chain: 10941 (2003) (0)
Problem 11390 (2008) (0)
4 M ay 2 00 5 Li Coefficients for Automorphic L-Functions (2004) (0)
ec 2 00 7 Cyclic Systems of Simultaneous Congruences (2009) (0)
On Sets of Integers Which Are Both Sum-Free and Product-Free (2012) (0)
Problem 11355 (2008) (0)
On the distribution of multiplicative translates of sets of residues (mod p) (1994) (0)
Ronald Lewis Graham (1935–2020) (2021) (0)
Conway’s Mathematics After Conway (2022) (0)
The error term in the truncated Perron formula for the logarithm of an -function (2022) (0)
The Distribution of 3 x + 1 Trees (2007) (0)
0 M ay 2 00 7 Ternary Expansions of Powers of 2 (2007) (0)
On Toric Orbits in the Affine Sieve (2018) (0)
A ug 2 00 9 The 3 x + 1 Problem : An Annotated Bibliography ( 1963 – 1999 ) (2009) (0)
Advanced Problems: 6399-6402 (1982) (0)
The Number of Triangles Needed to Span a Polygon Embedded in R^d (2002) (0)
ERRATUM: "CYCLIC SYSTEMS OF SIMULTANEOUS CONGRUENCES" (2010) (0)
The Lerch zeta function IV. Hecke operators (2016) (0)
On a Class of Balancing Games (2003) (0)
On the Riemann Hypothesis for Weng’s non-abelian zeta of rank 2 (2015) (0)
Class field theory for orders of number fields (2022) (0)
N T ] 1 1 Se p 20 00 Apollonian Circle Packings : Number Theory (2000) (0)
Advanced Problems: 6339-6343 (1981) (0)
Modular Fekete Polynomials: 10479 (1998) (0)
Comment on: Absolute Derivations and Zeta Functions (2004) (0)
$3x+1$ inverse orbit generating functions almost always have natural boundaries (2014) (0)
Partial Factorizations of Generalized Binomial Products (2021) (0)
Polynomial Splitting Measures and Cohomology of the Pure Braid Group (2017) (0)
Elementary Problems: E3129-E3134 (1986) (0)
2 6 Ja n 20 06 Zero Spacing Distributions for Differenced L-Functions (2006) (0)
Problem 10822 (2000) (0)
Symbolic dynamics of path sets (2012) (0)
The Takagi Function and Related Functions (2010) (0)

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