Tom M. Apostol | Academic Influence

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According to Wikipedia, Tom Mike Apostol was an American analytic number theorist and professor at the California Institute of Technology, best known as the author of widely used mathematical textbooks. Life and career Apostol was born in Helper, Utah. His parents, Emmanouil Apostolopoulos and Efrosini Papathanasopoulos, were Greek immigrants. Apostolopoulos's name was shortened to Mike Apostol when he obtained his United States citizenship, and Tom Apostol inherited this Americanized surname.

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Tom M. Apostol'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 Papers

Introduction to analytic number theory (1976) (3600)
Mathematical Analysis (1957) (2026)
Modular Functions and Dirichlet Series in Number Theory (1976) (1156)
On the Lerch zeta function. (1951) (427)
One-variable calculus, with an introduction to linear algebra (1967) (208)
Generalized Dedekind sums and transformation formulae of certain Lambert series (1950) (169)
An Elementary View of Euler's Summation Formula (1999) (141)
Multi-variable calculus and linear algebra, with applications to differential equations and probability (1969) (126)
Mathematical analysis : a modern approach to advanced calculus / Tom M. Apostol (1957) (112)
Book Reviews: Mathematical Analysis. A Modern Approach to Advanced Calculus (1958) (79)
Arithmetical properties of generalized Ramanujan sums (1972) (78)
Another elementary proof of Euler''s formula for (2 ) n z (1973) (72)
Dirichlet series related to the Riemann zeta function (1984) (61)
Resultants of cyclotomic polynomials (1970) (55)
The evaluation of Ramanujan’s sum and generalizations (1953) (53)
A proof that euler missed: evaluating ζ(2) the easy way (1983) (53)
Theorems on generalized Dedekind sums (1952) (52)
Formulas for higher derivatives of the Riemann zeta function (1985) (49)
Calculus, Volume 1 (1961) (47)
Zeta and related functions (2010) (40)
Irrationality of The Square Root of Two—A Geometric Proof (2000) (37)
Calculus, Volume 1: One-Variable Calculus with an Introduction to Linear Algebra (1961) (34)
A Primer on Bernoulli Numbers and Polynomials (2008) (33)
Calculus, Volume II. (1962) (32)
Explicit Formulas for Solutions of the Second-Order Matrix Differential Equation Y″ = ay (1975) (29)
Dirichlet L-functions and character power sums (1970) (27)
A New Method for Investigating Euler Sums (2000) (26)
Sums of Squares of Distances in m-Space (2003) (24)
Identities for sums of Dedekind type (1982) (24)
Some Explicit Formulas for the Exponential Matrix etA (1969) (24)
Elementary proofs of Berndt’s reciprocity laws (1982) (23)
Unwrapping Curves from Cylinders and Cones (2007) (22)
Beyond the Mechanical Universe: From Electricity to Modern Physics (1986) (21)
New Horizons in Geometry (2013) (21)
The resultant of the cyclotomic polynomials _{}() and _{}() (1975) (19)
Some Properties of Completely Multiplicative Arithmetical Functions (1971) (19)
The Tunnel of Samos (2004) (18)
Addendum to ‘On the Lerch zeta function’ (1952) (17)
The Mechanical Universe: Introduction to Mechanics and Heat (1985) (17)
The approximate functional equation of Hecke’s Dirichlet series (1957) (16)
Some series involving the Riemann zeta function (1954) (15)
Ptolemy's Inequality and the Chordal Metric (1967) (14)
Möbius functions of order k (1970) (14)
Solids Circumscribing Spheres (2006) (14)
A Fresh Look at the Method of Archimedes (2004) (14)
A Visual Approach to Calculus Problems (2000) (13)
Calculating Higher Derivatives of Inverses (2000) (12)
A Course in Mathematical Analysis, Vol. II. (1965) (12)
Elementary proof of the transformation formula for Lambert series involving generalized Dedekind sums (1982) (11)
Subtangents—An Aid to Visual Calculus (2002) (10)
The Mechanical Universe: Introduction to Mechanics and Heat and Beyond the Mechanical Universe: From Electricity to Modern Physics and The Mechanical Universe: Mechanics and Heat (Advanced Edition) (1986) (10)
Figures Circumscribing Circles (2004) (10)
Euler’s -function and separable Gauss sums (1970) (10)
A New Look at the So-Called Trammel of Archimedes (2009) (9)
On the functional equation $F(mn)F((m,\,n))=F(m)F(n)f((m,\,n))$. (1964) (9)
The method of sweeping tangents (2008) (9)
Tangents and Subtangents Used to Calculate Areas (2002) (9)
Tanvolutes: Generalized Involutes (2010) (9)
Calculus vol. 1 : one-variable calculus with an introduction to linear algebra / Tom M. Apostol (1967) (8)
Linear Algebra: A First Course with Applications to Differential Equations (1997) (8)
Calculus, volume II : multi - variable and linear algebra, with application to differential equations and probability / Tom M. Apostol (1969) (8)
Calculus of several variables with applications to probability and vector analysis (1962) (8)
Finding Centroids the Easy Way (8)
Dirichlet $L$-functions and primitive characters (1972) (7)
Identities involving the coefficients of certain Dirichlet series (1951) (7)
Remark on the Hurwitz zeta function (1951) (7)
The Story of PI (1989) (7)
Selected papers on calculus (1971) (6)
Sums of Squares of Distances (2001) (5)
The Dedekind eta function (1976) (5)
New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors (2008) (5)
An extension of the Lehmers’ picturesque exponential sums (1993) (5)
A Centennial History of the Prime Number Theorem (2000) (5)
Isoperimetric and Isoparametric Problems (2004) (5)
Teaching Mathematics with Computer Animated Videotapes. (1991) (4)
Centroids Constructed Graphically (2004) (4)
The Fundamental Theorem of Arithmetic (1976) (4)
Analytic Proof of the Prime Number Theorem (1976) (4)
Binary vectors with prescribed subsets of consecutive ones (1988) (4)
A short proof of Shô Iseki’s functional equation (1964) (4)
Term-Wise Differentiation of Power Series (1952) (3)
ENERGY: CONSERVATION AND CONVERSION (1986) (3)
New Insight into Cycloidal Areas (2009) (3)
Volume/Surface Area Relations for n-Dimensional Spheres, Pseudospheres, and Catenoids (2015) (3)
Another Elementary Proof of Euler ' s Formula for ζ ( 2 n ) Author ( s ) : (2010) (3)
A Century Of Calculus (1992) (3)
90.36 Bernoulli’s power-sum formulas revisited (2006) (3)
What Is the Most Surprising Result in Mathematics? Part II (1997) (3)
Computer Animated Mathematics Videotapes (2002) (3)
Surprising Geometric Properties of Exponential Functions (1998) (3)
Rademacher’s series for the partition function (1976) (2)
New Balancing Principles Applied to Circumsolids of Revolution, and to n-Dimensional Spheres, Cylindroids, and Cylindrical Wedges (2013) (2)
On magic squares constructed by the uniform step method (1951) (2)
Introduction, with vectors and analytic geometry (1961) (2)
Cycloidal Areas without Calculus (1999) (2)
The Mechanical Universe: Preface (1986) (2)
What Is the Most Surprising Result in Mathematics (1996) (2)
Area & Arc Length of Trochogonal Arches (2003) (2)
New Horizons in Geometry: Bibliography (2012) (1)
A Characteristic Property of the Mobius Function (1965) (1)
Averages of Arithmetical Functions (1976) (1)
Some Elementary Theorems on the Distribution of Prime Numbers (1976) (1)
Asymptotic Series Related to the Partition Function (1951) (1)
On the nonvanishing of homogeneous product sums (1986) (1)
A Note on Periodic Completely Multiplicative Arithmetical Functions (1976) (1)
Identities for series of the type Σ()() (1973) (1)
The modular group and modular functions (1976) (1)
Functions of number theory (2010) (1)
Dirichlet’s Theorem on Primes in Arithmetical Progressions (1976) (1)
General Dirichlet series and Bohr’s equivalence theorem (1976) (1)
Sums of squares of integers in arithmetic progression (2011) (1)
Proof Without Words: Surprising Property of Hyperbolas (2006) (1)
Ode to andrew wiles, kbe (2000) (1)
Complete Dissections: Converting Regions and Their Boundaries (2011) (1)
Ellipse to Hyperbola: “With This String I Thee Wed” (2011) (1)
New Horizons in Geometry: Unwrapping Curves from Cylinders and Cones (2012) (1)
87.02 Sums of consecutive positive integers (2003) (1)
Generalized Cyclogons (2002) (1)
Kronecker’s theorem with applications (1976) (1)
Volumes of solids swept tangentially around cylinders (2015) (1)
Elementary Problems: E2438-E2443 (1973) (0)
Sines and Cosines. Part 3 of 3 (1992) (0)
Early History of Mathematics (2003) (0)
Volume/Surface Area Ratios for Globes, with Applications (2015) (0)
Surprisingly Accurate Rational Approximations (2002) (0)
New Horizons in Geometry: Preface (2012) (0)
Note on the trivial zeros of Dirichlet $L$-functions (1985) (0)
New Horizons in Geometry: Ellipse to Hyperbola: “With This String I Thee Wed” (2012) (0)
Good Rational Approximations to Logarithms (2001) (0)
The Method of Punctured Containers (2007) (0)
New Horizons in Geometry: Isoperimetric and Isoparametric Problems (2012) (0)
THE DECEMBER MEETING IN PASADENA The four hundred seventy-sixth meeting of the American (2007) (0)
Beyond the Mechanical Universe (2008) (0)
THE JUNE MEETING IN EUGENE The four hundred eight-second meeting of the American Mathe- (2007) (0)
A Glance at the World (2010) (0)
Modular forms with multiplicative coefficients (1976) (0)
Problems for Solution: 4693-4697 (1956) (0)
Periodic Arithmetical Functions and Gauss Sums (1976) (0)
The Mechanical Universe: INTRODUCTION TO THE MECHANICAL UNIVERSE (Program 1) (1986) (0)
Index To Volume 120, 2013 (2013) (0)
EULER SUMS REVISITED (2003) (0)
The Functions ζ(s) and L(s, χ) (1976) (0)
New Horizons in Geometry: New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors (2012) (0)
The Mechanical Universe: THE INTERNATIONAL SYSTEM OF UNITS (1986) (0)
THE CONSERVATION OF MOMENTUM (1986) (0)
New Horizons in Geometry: New Balancing Principles with Applications (2012) (0)
TEMPERATURE AND THE GAS LAWS (1986) (0)
The Mechanical Universe: KEPLER'S LAWS AND THE CONIC SECTIONS (1986) (0)
THE QUEST FOR LOW TEMPERATURE (1986) (0)
THE ENGINE OF NATURE (1986) (0)
New Horizons in Geometry: Cyclogons and Trochogons (2012) (0)
Grassroots Democratic Activism in Altadena, California, in the Mid-Twentieth Century (2014) (0)
The Mechanical Universe: THE LAW OF FALLING BODIES (Program 2) (1986) (0)
Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series (2019) (0)
Summing the Initial Inverted Powers: 11128 (2007) (0)
Triangles in Rectangles (1998) (0)
New Horizons in Geometry: Circumgons and Circumsolids (2012) (0)
NAVIGATING IN SPACE (1986) (0)
New Horizons in Geometry: Appendix (2012) (0)
New Horizons in Geometry: Foreword (2012) (0)
Finite Abelian Groups and Their Characters (1976) (0)
KEPLER'S LAWS AND THE CONIC SECTIONS (Program 21) (1985) (0)
New Horizons in Geometry: Centroids (2012) (0)
Quadratic Residues and the Quadratic Reciprocity Law (1976) (0)
Video Based Hypermedia for Communicating Mathematics (2003) (0)
Problems for Solution: 4473-4477 (1952) (0)
The Mechanical Universe: ROTATIONAL DYNAMICS FOR RIGID BODIES (1986) (0)
UNIVERSAL GRAVITATION AND CIRCULAR MOTION (1986) (0)
The Mechanical Universe: ANGULAR MOMENTUM (1986) (0)
Arithmetical Functions and Dirichlet Multiplication (1976) (0)
Congruences for the coefficients of the modular function j (1976) (0)
THE APPROXIMATE FUNCTIONAL EQUATION OF (2016) (0)
THE LANGUAGE OF NATURE: DERIVATIVES AND INTEGRALS (1986) (0)
The Mechanical Universe: SELECTED BIBLIOGRAPHY (1986) (0)
The Mechanical Universe: SOLVING THE KEPLER PROBLEM (1986) (0)
New Horizons in Geometry: The Method of Punctured Containers (2012) (0)
A New Look at Surfaces of Constant Curvature (2016) (0)
Volumes of Solids Swept Tangentially Around General Surfaces (2015) (0)
Topological Treatment of Platonic , Archimedean , and Related Polyhedra (2015) (0)
The Mechanical Universe: NEWTON'S LAWS AND EQUILIBRIUM (1986) (0)
The Mechanical Universe: VECTORS (1986) (0)
New Horizons in Geometry: Arclength and Tanvolutes (2012) (0)
New Horizons in Geometry: Cycloids and Trochoids (2012) (0)
Calculus vol. 2 : multi-variabel calculus and linear algebra, with applications to differential equations and probability / Tom M. Apostol (1969) (0)
Index to the Mathematical Gazette (2006) (0)
New Horizons in Geometry: Introduction (2012) (0)
New Horizons in Geometry: Trammels (2012) (0)
FORCES IN ACCELERATING REFERENCE FRAMES (1986) (0)
ANGULAR MOMENTUM (Program 19) (1985) (0)
Visualization in Learning Mathematics with Hypervideo: The Story of Pi demo (2005) (0)
Dirichlet Series and Euler Products (1976) (0)
Primitive character sums and Dirichlet L-functions† (1978) (0)
Linear Algebra (1997) (0)
New Horizons in Geometry: Sums of Squares (2012) (0)
Problems for Solution: E1001-E1005 (1952) (0)
Sums of consecutive positive integers (2003) (0)
FORMULAS FROM ALGEBRA, GEOMETRY, AND TRIGONOMETRY (1986) (0)
THE APRIL MEETING IN BERKELEY The four hundred thirty-sixth meeting of the American Mathe - (2007) (0)
New Horizons in Geometry: Mamikon's Sweeping Tangent Theorem (2012) (0)
New Horizons in Geometry: About the Authors (2012) (0)
The Tunnels of Samos (1995) (0)

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