Hugh Lowell Montgomery | Academic Influence

Hugh Lowell Montgomery's AcademicInfluence.com Rankings

Hugh Lowell Montgomery

Mathematics

#406

World Rank

#822

Historical Rank

#185

USA Rank

Measure Theory

#1817

World Rank

#2223

Historical Rank

#571

USA Rank

mathematics Degrees

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Mathematics

Hugh Lowell Montgomery's Degrees

PhD Mathematics Princeton University
Masters Mathematics Stanford University

Why Is Hugh Lowell Montgomery Influential?

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According to Wikipedia, Hugh Lowell Montgomery is an American mathematician, working in the fields of analytic number theory and mathematical analysis. As a Marshall scholar, Montgomery earned his Ph.D. from the University of Cambridge. For many years, Montgomery has been teaching at the University of Michigan.

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Hugh Lowell Montgomery'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

Multiplicative Number Theory I: Classical Theory (2006) (795)
Topics in Multiplicative Number Theory (1971) (713)
Ten lectures on the interface between analytic number theory and harmonic analysis (1994) (693)
Hilbert’s inequality (1974) (308)
Primes in Short Intervals (2004) (185)
The large sieve (1973) (185)
The analytic principle of the large sieve (1978) (179)
A bound for the least prime ideal in the Chebotarev Density Theorem (1979) (178)
The exceptional set in Goldbach''s problem (1975) (165)
Extreme values of the Riemann zeta function (1977) (129)
Pair Correlation of Zeros and Primes in Short Intervals (1987) (124)
Minimal theta functions (1988) (119)
Zeros of the derivatives of the Riemann zeta-function (1974) (112)
Algebraic integers near the unit circle (1971) (96)
Exponential sums with multiplicative coefficients (1977) (93)
Products of polynomials in many variables (1990) (89)
Large deviations of sums of independent random variables (1988) (60)
Notes on small class numbers (1974) (59)
Extreme values of Dirichlet L-functions at 1 (1999) (53)
Multiplicative Number Theory I: Zeros (2006) (52)
On the distribution of reduced residues (1986) (52)
Mean values of multiplicative functions (2002) (49)
Primes in arithmetic progressions. (1970) (47)
Fluctuations in the mean of Euler’s phi function (1987) (42)
Mean and large values of Dirichlet polynomials (1969) (42)
Beyond pair correlation (2000) (41)
Zeros of approximations to the zeta function (1983) (40)
Note on a Diophantine inequality in several variables (2000) (39)
Zeros ofL-functions (1969) (39)
Beurling primes with large oscillation (2006) (38)
Mean values of the logarithmic derivative of the Riemann zeta-function with applications to primes in short intervals (2001) (38)
On the $L$-functions of canonical Hecke characters of imaginary quadratic fields, II (1980) (37)
An exponential polynomial formed with the Legendre symbol (1980) (31)
Some remarks on Gauss sums associated with kth powers (1995) (29)
ERROR TERMS IN ADDITIVE PRIME NUMBER THEORY (1973) (27)
A Note on the Large Sieve (1968) (26)
Real quadratic fields with large class number (1977) (26)
Multiplicative Number Theory I: Contents (2006) (24)
Oscillations of Quadratic L-Functions (1990) (20)
Kronecker’s approximation theorem (2016) (18)
A Tribute to Paul Erdős: On the Erdős–Fuchs theorems (1990) (17)
On zeros of $p$-adic forms. (1983) (17)
Exploring the Riemann Zeta Function (2017) (17)
Harmonic Analysis as found in Analytic Number Theory (2001) (14)
Changes of sign of the error term in the prime number theorem (2006) (14)
Early Fourier Analysis (2014) (14)
Distribution of irregular primes (1965) (13)
Exploring the Riemann Zeta Function : 190 years from Riemann's Birth (2017) (12)
A note on rearrangements of Fourier coefficients (1976) (10)
The order of magnitude of the mth coefficients of cyclotomic polynomials (1985) (10)
Elementary Problems: E3301-E3306 (1989) (9)
A further generalization of Hilbert's inequality (1999) (9)
Zeros of a Family of Approximations of the Riemann Zeta-Function (2013) (8)
A Heuristic for the Prime Number Theorem (2006) (7)
Geometric properties of the zeta function (2012) (5)
Selberg's Work on the Zeta-Function (1989) (5)
Biased Trigonometric Polynomials (2007) (4)
Polynomials in many variables (1976) (3)
EXTREME VALUES OF THE ZETA FUNCTION AT CRITICAL POINTS (2016) (3)
Greedy sums of distinct squares (2004) (3)
Elementary Problems: E2546-E2551 (1975) (3)
On a question of Ramachandra (1982) (2)
Multiplicative Number Theory I: List of notation (2006) (2)
Spirals of the Zeta Function I (2015) (2)
Small polynomials with integral coefficients (chapter 10) (1994) (1)
The bombieri — Vinogradov theorem and other applications of the large sieve (1971) (1)
Small gaps and small spacings between zeta zeros (2022) (1)
The combinatorics of moment calculations (2010) (1)
Prime-like sequences (1988) (1)
Elementary Problems: E2744,E2779-E2784 (1979) (1)
Moments of a Thue–Morse generating function (2018) (1)
The mean value theorem of Barban (1971) (0)
Multiplicative Number Theory I: Topics in harmonic analysis (2006) (0)
Elementary Problems: E2755-E2760 (1979) (0)
Irregularities of distribution (chapter 6) (1994) (0)
Exponential sums. II: Vinogradov’s method (chapter 4) (1994) (0)
Multiplicative Number Theory I: Preface (2006) (0)
A dictionary of political phrases and allusions, with a short bibliography (2010) (0)
Multiplicative Number Theory I: Primitive characters and Gauss sums (2006) (0)
More information 1 Dirichlet series : I 1 . 1 Generating functions and asymptotics (2011) (0)
Advanced Problems: 6198-6203 (1978) (0)
Advanced Problems: 6132-6137 (1977) (0)
An introduction to Turan’s method (chapter 5) (1994) (0)
Multiplicative Number Theory I: Further discussion of the Prime Number Theorem (2006) (0)
Mean and large values of Dirichlet polynomials (chapter 7) (1994) (0)
Low moments of Dirichlet series (2014) (0)
A Generalization of Ehrenfeucht ’ s Irreducibility Criterion (2003) (0)
Multiplicative Number Theory I: Explicit formulæ (2006) (0)
Uniform distribution (chapter 1) (1994) (0)
Classical mean value theorems (1971) (0)
Elementary Problems: E2743-E2748 (1978) (0)
Zero-free regions and the proliferation of zeros (1971) (0)
A lemma in additive prime number theory (1971) (0)
Advanced Problems: 6072-6077 (1976) (0)
Dirichlet series: II (2006) (0)
Elementary Problems: E2495,E2516-E2521 (1975) (0)
Elementary Problems: E2605-E2610 (1976) (0)
Random Matrix Theory Predictions for the Asymptotics of the Moments of the Riemann Zeta Function and Numerical Tests of the Predictions (2006) (0)
Multiplicative Number Theory I: The elementary theory of arithmetic functions (2006) (0)
Multiplicative Number Theory I: The Riemann–Stieltjes integral (2006) (0)
The mean values of logarithms of algebraic integers (2017) (0)
A weighted sieve and its application (1971) (0)
THE ANALYTIC PRINCIPLE OF THE LARGE SIEVE BY HUGH L. MONTGOMERY (2007) (0)
Mathematische Annalen Beurling primes with large oscillation (2005) (0)
Exponential sums. I: The methods of Weyl and van der Corput (chapter 3) (1994) (0)
Multiplicative Number Theory I: The Prime Number Theorem (2006) (0)
Multiplicative Number Theory I: The gamma function (2006) (0)
Turán’swork in analytic number theory (2013) (0)
Workshop: Analytic Number Theory Table of Contents (2014) (0)
ON MULTIPLICATIVE COMPOSITIONS of INTEGERS (2017) (0)
“Counting”: A query (1965) (0)
The prime number theorems of Hoheisel and Selberg (1971) (0)
New mean value theorems (1971) (0)
Low moments of Dirichlet series (2014) (0)
Multiplicative Number Theory I: Oscillations of error terms (2006) (0)
Multiplicative Number Theory I: Primes in arithmetic progressions: II (2006) (0)
Distribution of zeros of L-functions (1971) (0)
Moments of a Thue–Morse generating function (2018) (0)
Sums of Numbers with Many Divisors (1999) (0)
Review: H. H. Halberstam and H.-E. Richert, Sieve methods (1976) (0)
Communications in Mathematical Physics Primes in Short Intervals (2004) (0)
Multiplicative Number Theory I: Conditional estimates (2006) (0)
Local variation of Euler products (2008) (0)
Large moduli theorems (1971) (0)
Further results and conjectures concerning mean and large moduli (1971) (0)
Least character non-residues and arg L(12+it, x) (1971) (0)
SIXTH ANNUAL UPSTATE NEW YORK NUMBER THEORY CONFERENCE APRIL 30 - MAY 1, 2016 ABSTRACTS Plenary Talks (2016) (0)
GMJ volume 30 issue 1 Cover and Front matter (1988) (0)
Multiplicative Number Theory I: Principles and first examples of sieve methods (2006) (0)
Mathematisches Forschungsinstitut Oberwolfach Report No . 46 / 2004 Theory of the Riemann Zeta and Allied Functions Organised (2006) (0)
Elementary Problems: E2558-E2563 (1975) (0)
Zeros of L-functions (chapter 9) (1994) (0)
Distribution of reduced residue classes in short intervals (chapter 8) (1994) (0)
Multiplicative Number Theory I: Analytic properties of the zeta function and L -functions (2006) (0)
Elementary Problems: E3201-E3206 (1987) (0)
Arithmetic formulations of the large sieve (1971) (0)
Mean moduli of L-functions (1971) (0)
Positivity of a Certain Power Series: 10870 (2003) (0)
van der Corput sets (chapter 2) (1994) (0)
Multiplicative Number Theory I: Dirichlet series: II (2006) (0)
Multiplicative Number Theory I: Bernoulli numbers and the Euler–MacLaurin summation formula (2006) (0)
A lower bound of Roth (1971) (0)
L 2 Majorant Principles (2013) (0)
Multiplicative Number Theory I: Applications of the Prime Number Theorem (2006) (0)
The Decimal Expansions of Powers of 9: 10758 (2001) (0)

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