Maruti Ram Murty

Maruti Ram Murty's AcademicInfluence.com Rankings

Maruti Ram Murty

Mathematics

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Graph Theory

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Number Theory

#170

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#223

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Measure Theory

#1129

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#1445

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Mathematics

Maruti Ram Murty's Degrees

Bachelors Mathematics Delhi University

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Maruti Ram Murty's Published Works

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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

Ramanujan Graphs (1965) (1200)
Problems in analytic number theory (2000) (237)
Mean values of derivatives of modular L-series (1991) (160)
A remark on Artin's conjecture (1984) (145)
On a Conjecture of Birch and Swinnerton-Dyer (2005) (143)
Non-vanishing of L-Functions and Applications (1997) (132)
Problems in algebraic number theory (1998) (118)
Oscillations of Fourier coefficients of modular forms (1983) (115)
Modular Forms and the Chebotarev Density Theorem (1996) (108)
Artin’s conjecture for primitive roots (1988) (87)
Transcendental values of the digamma function (2007) (74)
Introduction to p-adic analytic number theory (2002) (62)
Selberg’s conjectures and Artin -functions (1994) (59)
Cyclicity of elliptic curves modulo p and elliptic curve analogues of Linnik’s problem (2004) (58)
Exponents of Class Groups of Quadratic Fields (1999) (54)
On the Enumeration of Finite Groups (1987) (53)
Transcendental values of certain Eichler integrals (2011) (53)
Sudoku Squares and Chromatic Polynomials (2007) (52)
Prime divisors of Fourier coefficients of modular forms (1984) (51)
Euclidean Rings of Algebraic Integers (2004) (48)
On the Distribution of Supersingular Primes (1996) (44)
Effective equidistribution of eigenvalues of Hecke operators (2009) (44)
STRONG MULTIPLICITY ONE FOR SELBERG'S CLASS (1994) (43)
Prime Numbers and Irreducible Polynomials (2002) (43)
An Introduction to Sieve Methods and Their Applications: Preface (2006) (41)
On Artin's conjecture (1983) (41)
Euler–Lehmer constants and a conjecture of Erdös (2010) (39)
The Square Sieve and the Lang–Trotter Conjecture (2005) (39)
The pair correlation of zeros of functions in the Selberg class (1999) (34)
Counting integral ideals in a number field (2007) (33)
Analytic Number Theory: Congruences between Modular Forms (1997) (31)
On the number of real quadratic fields with class number divisible by 3 (2002) (31)
Ramanujan series for arithmetical functions (2013) (31)
SPECIAL VALUES OF THE POLYGAMMA FUNCTIONS (2009) (30)
Odd values of the Ramanujan $\tau $-function (1987) (29)
The abc conjecture and non-Wieferich primes in arithmetic progressions (2013) (28)
ON A CONJECTURE OF ERD ˝ OS (2012) (26)
Multiple Hurwitz Zeta Functions (2006) (26)
Primes in Certain Arithmetic Progressions (2006) (25)
Explicit formulas for the pair correlation of zeros of functions in the Selberg class (2002) (25)
Cyclicity and generation of points modp on elliptic curves (1990) (24)
Bounds for congruence primes (1999) (24)
On the order of (mod ) (1999) (23)
Elliptic Curves and Related Topics (1994) (23)
Transcendental values of class group L-functions (2011) (22)
Averages of exponential twists of the Liouville function (2002) (22)
A derivation of the Hardy-Ramanujan formula from an arithmetic formula (2012) (21)
VARIATIONS ON A THEME OF ROMANOFF (1996) (21)
Sign changes of Fourier coefficients of half-integral weight cusp forms (2014) (21)
On the Rédei zeta function (1980) (20)
The ABC conjecture and prime divisors of the Lucas and Lehmer sequences (2000) (20)
A problem of Chowla revisited (2011) (20)
The Sato – Tate conjecture and generalizations ∗ (19)
The Euclidean algorithm for Galois extensions of Q. (1995) (19)
A note on quadratic twists of an elliptic curve (1994) (19)
ODD VALUES OF FOURIER COEFFICIENTS OF CERTAIN MODULAR FORMS (2007) (19)
Non-Abelian Generalizations of the Erdős-Kac Theorem (2004) (19)
Problems in the Theory of Modular Forms (2015) (18)
Modular forms and effective Diophantine approximation (2013) (18)
On groups of squarefree order (1984) (17)
A Bombieri-Vinogradov theorem for all number fields (2012) (16)
Pick's Theorem via Minkowski's Theorem (2007) (16)
The uncertainty principle and a generalization of a theorem of Tao (2012) (16)
On the supersingular reduction of elliptic curves (1987) (16)
On the estimation of eigenvalues of Hecke operators (1985) (16)
Finite Ramanujan expansions and shifted convolution sums of arithmetical functions (2016) (16)
The ABC conjecture and exponents of class groups of quadratic fields (1998) (15)
A SIMPLE DERIVATION OF ζ ( 1 − k ) = − Bk / k (2008) (15)
On Kummer's Conjecture☆ (2001) (15)
Twin primes and the parity problem (2017) (15)
ALGEBRAIC INDEPENDENCE OF VALUES OF MODULAR FORMS (2011) (15)
Elliptic curves and modular forms (1991) (13)
THE CLASS NUMBER OF Q ( √− p ) AND DIGITS OF 1 /p (2010) (13)
A family of number fields with unit rank at least 4 that has Euclidean ideals (2013) (13)
Supersingular primes common to two elliptic curves (1995) (13)
On the error term in a Parseval type formula in the theory of Ramanujan expansions II (2015) (13)
Uniform Distribution of Zeros of Dirichlet Series (2007) (13)
L-series of automorphic forms on GL(3,R) (1989) (12)
Oscillations of coefficients of Dirichlet series attached to automorphic forms (2014) (12)
The Mathematical Legacy of Srinivasa Ramanujan (2012) (12)
Sieve Methods, Exponential Sums, and their Applications in Number Theory: Artin's Conjecture and Elliptic Analogues (1997) (12)
Non-vanishing of Dirichlet series with periodic coefficients (2014) (12)
Artin’s Conjecture for Polynomials Over Finite Fields (2000) (12)
Transcendence of the log gamma function and some discrete periods (2009) (11)
Linear independence of Hurwitz zeta values and a theorem of Baker-Birch-Wirsing over number fields (2012) (11)
On Simple Zeros of Certain L-Series (1990) (11)
AN ANALOGUE OF THE ERDÖS-KAK THEOREM FOR FOURIER COEFFICIENTS OF MODULAR FORMS (2011) (11)
A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences (2017) (11)
Transcendental values of the p-adic digamma function (2008) (11)
Transcendental values of class group L-functions, II (2012) (11)
PRIME NUMBERS IN CERTAIN ARITHMETIC PROGRESSIONS (2008) (10)
The Fibonacci Zeta Function (2013) (10)
Elliptic curves, L-functions, and Hilbert's tenth problem (2018) (10)
Distinguishing Hecke eigenforms (2016) (10)
On a Problem of Ruderman (2011) (10)
An Introduction to Sieve Methods and Their Applications: Frontmatter (2005) (10)
Linear independence of digamma function and a variant of a conjecture of Rohrlich (2009) (10)
On the number of groups of a given order (1984) (9)
THE GENERALIZED ARTIN CONJECTURE AND ARITHMETIC ORBIFOLDS (2007) (9)
Effective equidistribution and the Sato–Tate law for families of elliptic curves ☆ (2010) (9)
AN ASYMPTOTIC FORMULA FOR THE COEFFICIENTS OF j(z) (2013) (9)
An Ω-theorem for Ramanujan's τ-function (1982) (9)
Sieve methods in combinatorics (2005) (9)
Irreducibility of Hecke polynomials (2003) (9)
An analogue of Artin's conjecture for Abelian extensions (1984) (8)
Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms (2018) (8)
COUNTING SQUAREFREE DISCRIMINANTS OF TRINOMIALS UNDER ABC (2008) (8)
A remark on a conjecture of Chowla (2018) (8)
A First Course in Graph Theory and Combinatorics (2009) (8)
A simple derivation of $\zeta(1-K)=-B_K/K$ (2000) (7)
Counting squarefree values of polynomials with error term (2014) (7)
Non-Vanishing of Quadratic Twists of Modular L -Functions (1997) (7)
A vanishing criterion for Dirichlet series with periodic coefficients (2018) (7)
Base change and the Birch-Swinnerton-Dyer conjecture (1993) (7)
ON THE TRANSCENDENCE OF CERTAIN INFINITE SERIES (2011) (7)
Ramanujan graphs and zeta functions (2005) (7)
On the asymptotics for invariants of elliptic curves modulo p (2012) (7)
FACTORING NEWPARTS OF JACOBIANS OF CERTAIN MODULAR CURVES (2010) (7)
On the Uniform Distribution of Certain Sequences (2003) (7)
Ramanujan's Proof of Bertrand's Postulate (2013) (6)
A PROBLEM OF FOMENKO'S RELATED TO ARTIN'S CONJECTURE (2012) (6)
A Generalization of Euler's Theorem for ζ(2k) (2016) (6)
The Euclidean algorithm for number fields and primitive roots (2012) (6)
GROUP STRUCTURE OF ELLIPTIC CURVES OVER FINITE FIELDS AND APPLICATIONS (2006) (6)
SOME VARIATIONS ON THE DEDEKIND CONJECTURE (2006) (6)
A higher rank Selberg sieve with an additive twist and applications (2017) (6)
On the Sieve of Eratosthenes (1987) (6)
Some Remarks on the Discrete Uncertainty Principle (2016) (5)
Review: S. J. Patterson, An introduction to the theory of the Riemann zeta-function, and A. G. Postnikov, Introduction to analytic number theory (1989) (5)
The Ramanujan τ -Function (2013) (5)
Summation methods and distribution of eigenvalues of Hecke operators (2008) (5)
Dirichlet series and hyperelliptic curves (2007) (5)
Some remarks related to Maeda's conjecture (2016) (5)
Irrational Numbers arising from Certain Differential Equations (1977) (5)
Bertrand's Postulate for Number Fields (2015) (5)
Some results in number theory, I (1979) (5)
Transcendence of Generalized Euler Constants (2013) (5)
Generalization of an identity of Ramanujan (2016) (4)
Diophantine m-tuples with the property D(n) (2019) (4)
The Paley graph conjecture and Diophantine m-tuples (2020) (4)
Small solutions of polynomial congruences (2010) (4)
The Chebotarev density theorem and the pair correlation conjecture (2016) (4)
A note on special values of $L$-functions (2014) (4)
On a Generalization of Artin's Conjecture (2008) (4)
EVALUATION OF THE QUADRATIC GAUSS SUM (2017) (4)
SOME REMARKS ON A PROBLEM OF CHOWLA (2011) (4)
On a conjecture of Erdos (2012) (4)
On a conjecture of Erdős and certain Dirichlet series (2015) (4)
New developments on the twin prime problem and generalizations (2014) (4)
Transcendental sums related to the zeros of zeta functions (2018) (3)
Some Ω-results for Ramanujan’s τ-function (1982) (3)
On the Density of Various Classes of Groups (1983) (3)
Elliptic Pseudoprimes (2010) (3)
Generalization of a theorem of Hurwitz (2016) (3)
On the -adic series ∑_{=1}^{∞}^{}⋅! (2004) (3)
POLYNOMIALS ASSUMING SQUARE VALUES (2012) (3)
Divisors of Fourier coefficients of modular forms (2014) (3)
On the number of special numbers (2017) (3)
QUADRATIC RECIPROCITY VIA LINEAR ALGEBRA (2005) (3)
Special values of the Gamma function at CM points (2015) (3)
Special values of derivatives of $L$-series and generalized Stieltjes constants (2018) (3)
The Generalized Dedekind Determinant (2015) (3)
Transcendental numbers and special values of Dirichlet series (2018) (3)
An application of Mumford's gap principle (2004) (3)
Some Remarks on Automorphy and the Sato-Tate Conjecture (2015) (2)
Some remarks on iterated maps of natural numbers (2014) (2)
From the Birch and Swinnerton-Dyer conjecture to Nagao’s conjecture (2021) (2)
Artin L -Functions (1997) (2)
Admissible primes and Euclidean quadratic fields (2018) (2)
Central limit theorems for sums of quadratic characters, Hecke eigenforms, and elliptic curves (2019) (2)
On Zagier’s cusp form and the Ramanujan τ function (1994) (2)
Ramanujan Graphs: An Introduction (2021) (2)
Transcendence of Some Infinite Series (2014) (2)
THE ERROR TERM IN THE SATO–TATE THEOREM OF BIRCH (2019) (2)
The Partition Function Revisited (2013) (2)
An Introduction to Sieve Methods and Their Applications: The large sieve (2005) (2)
A variant of the Lang–Trotter conjecture (2012) (2)
Transcendental values of the incomplete gamma function and related questions (2015) (2)
Finitely generated groups (mod $p$) (1994) (2)
ON THE ASYMPTOTIC NATURE OF ELLIPTIC CURVES MODULO p ADAM TYLER FELIX AND M. RAM MURTY (2011) (2)
A variant of the Hardy-Ramanujan theorem (2022) (2)
MODULAR FORMS AND THE CHEBOTAREV (2016) (1)
18 Congruences between Modular Forms (2012) (1)
Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes (2019) (1)
On the parity of the Fourier coefficients of j -function (2015) (1)
The Six Exponentials Theorem (2014) (1)
Sieving Using Dirichlet Series (2002) (1)
Ramanujan and expander graphs (2013) (1)
Artin's primitive root conjecture for function fields revisited (2020) (1)
Variations of the Sato-Tate Conjecture (2009) (1)
On the normal number of prime factors of sums of Fourier coefficients of eigenforms (2021) (1)
An ~2-Theorem for Ramanujan's z-Function (1982) (1)
The analog of the Erdös distance problem in finite fields (2017) (1)
Relations between Certain Power Series and Functions Involving Zeros of Zeta Functions (2020) (1)
A remark on the Lang-Trotter and Artin conjectures (2018) (1)
A weighted Turán sieve method (2006) (1)
Primes in Arithmetic Progressions (2001) (1)
EXACT CONTROLLABILITY OF THE WAVE EQUATION IN FRACTIONAL ORDER SPACES (2014) (1)
Chapter 8 Suggestions for Further Reading (1997) (1)
The Prime Number Theorem (2001) (1)
Fundamental units and consecutive squarefull numbers (2017) (1)
The Okada space and vanishing of ${L(1,{f})}$ (2021) (1)
A Smooth Selberg Sieve and Applications (2016) (1)
On sign changes for almost prime coefficients of half-integral weight modular forms (2015) (1)
The Lindemann–Weierstrass Theorem (2014) (1)
Class Numbers of Quadratic Fields (2020) (1)
On the nature of eγ and non-vanishing of derivatives of L-series at s = 1/2 (2016) (1)
On THE ASYMPTOTIC FORMULA FOR THE FOURIER COEFFICIENTS OF THE J-Function (2016) (1)
Higher Reciprocity Laws (1999) (1)
The Selberg Class (2001) (1)
The Legacy of Srinivasa Ramanujan (2013) (1)
The Central Limit Theorem in Algebra and Number Theory (2020) (1)
Enumeration under Group Action (2009) (1)
THE CAUCHY-SCHWARZ INEQUALITY IN MATHEMATICS, PHYSICS AND STATISTICS (2019) (1)
The Sato–Tate Conjecture for the Ramanujan τ-Function (2013) (1)
A Second Course in Analysis (2022) (1)
An Introduction to Sieve Methods and Their Applications: Selberg's sieve (2005) (1)
TRANSCENDENTAL NUMBERS AND ZETA FUNCTIONS (2000) (1)
The Twin Prime Problem and Generalisations (2013) (1)
The twin prime problem and generalizations (après Yitang Zhang) (2013) (0)
Linear Independence of Values of Dirichlet L-Functions (2014) (0)
p-adic Methods (2001) (0)
Probabilistic Number Theory (2013) (0)
A localized Erdős-Kac theorem (2021) (0)
Book Review: An introduction to the theory of the Riemann zeta-function (1989) (0)
Algebraic Numbers and Integers (1999) (0)
Modular Forms of Level One (2016) (0)
Generalized Diophantine 𝑚-tuples (2021) (0)
On a paper of S S Pillai (2012) (0)
The Baker–Birch–Wirsing Theorem (2014) (0)
An Introduction to Sieve Methods and Their Applications: The lower bound sieve (2005) (0)
Book Review: Elementary methods in number theory (2000) (0)
Chapter 5 Dirichlet L-Functions (1997) (0)
Suggestions for Further Reading (1997) (0)
Ramanujan and Transcendence (2013) (0)
A note on q-analogues of Dirichlet L-functions (2016) (0)
A localized Erdős-Kac theorem for $\omega_y(p+a)$ (2023) (0)
The Ideal Class Group (1999) (0)
An Introduction to Sieve Methods and Their Applications: Some elementary sieves (2005) (0)
A note on values of the Dedekind zeta-function at odd positive integers (2021) (0)
Chapter 1 The Prime Number Theorem and Generalizations (1997) (0)
Erratum to: The Ramanujan τ -Function (2013) (0)
Corrigendum to "Artin's primitive root conjecture for function fields revisited" [Finite Fields Appl. 67 (2020) 101713] (2021) (0)
The Petersson Inner Product (2016) (0)
The Upper Half-Plane (2016) (0)
Special values of the Gamma function at CM points (2014) (0)
Modular Forms and Dirichlet Series (1997) (0)
Mathematics of the Pandemic (2021) (0)
The Zeta Mahler measure of $(z^n − 1)/(z − 1)$ (2019) (0)
Graphs and Gaps between Primes ∗ (2007) (0)
On Artin £-Functions (2018) (0)
The Modular Invariant (2014) (0)
Convolution of values of the Lerch zeta-function (2020) (0)
Selberg’s Conjectures (1997) (0)
THE GENERALIZED ARTIN CONJECTURE AND ARITHMETIC (2007) (0)
Ramanujan’s Conjecture and ℓ-Adic Representations (2013) (0)
Leopoldt’s formula for _{}(1,) (2009) (0)
Fermat quotients and the Ankeny-Artin-Chowla conjecture (2023) (0)
Transcendental Values of Some Dirichlet Series (2014) (0)
On a conjecture of Bateman about r5(n) (2019) (0)
Transcendental Values of the j-Function (2014) (0)
Preface special volume on the Conference on Graph Theory, Matrix Theory and Interactions (2015) (0)
The Method of Contour Integration (2001) (0)
The Maximum Modulus Principle and Its Applications (2014) (0)
On Hasse’s inequality (2023) (0)
The Modular Group (2016) (0)
On the density of irreducible polynomials which generate k-free polynomials over function fields (2022) (0)
An introduction to Iwasawa theory (2009) (0)
Chapter 3 Equidistribution and L-Functions (1997) (0)
Problem session (Chaired by Prof. P. Erdös) two problems proposed by K. Ramachandra (1982) (0)
An Introduction to Sieve Methods and Their Applications: The sieve of Eratosthenes (2005) (0)
The class number of $\mathbb{Q}(\sqrt{-p})$ and digits of $1/p$ (2011) (0)
The work of K. Ramachandra in algebraic number theory (2013) (0)
An Introduction to Sieve Methods and Their Applications: The normal order method (2005) (0)
Chapter 7 Selberg’s Conjectures (1997) (0)
Corrigendum to “Transcendence of the log gamma function and some discrete periods” [J. Number Theory 129 (9) (2009) 2154–2165] (2010) (0)
Arithmetic of the Partition Function (2013) (0)
Mock Theta Functions and Mock Modular Forms (2013) (0)
The Prime Number Theorem and Generalizations (1997) (0)
Hecke Operators of Higher Level (2016) (0)
Chapter 6 Non-Vanishing of Quadratic Twists of Modular L -Functions (1997) (0)
On the number of special numbers (2017) (0)
Finite order elements in the integral symplectic group (2017) (0)
On the transcendence of certain Petersson inner products (2017) (0)
Dirichlet Series and Modular Forms (2016) (0)
Some Applications of Baker’s Theorem (2014) (0)
Elliptic Integrals and Hypergeometric Series (2014) (0)
Transcendental values of the incomplete gamma function and related questions (2015) (0)
Matrices and Graphs (2009) (0)
Transcendence of Values of Modular Forms (2014) (0)
The Turán sieve (2005) (0)
Estimates for Derivatives (2014) (0)
Finite Fields and Their Applications (2020) (0)
The Circle Method (2013) (0)
Chapter 2 Artin L -Functions (1997) (0)
Modular Forms of Higher Level (2016) (0)
Edges and Cycles (2009) (0)
Some remarks on iterated maps of natural numbers (2014) (0)
Prime Numbers and Highly Composite Numbers (2013) (0)
Transcendental Values of Elliptic Functions (2014) (0)
Littlewood and number theory (2013) (0)
Basic Notions of Graph Theory (2009) (0)
Transcendental Values of Eisenstein Series (2014) (0)
Transcendental Values of Some Elliptic Integrals (2014) (0)
OF HALF-INTEGRAL WEIGHT CUSP FORMS (2013) (0)
Chapter 4 Modular Forms and Dirichlet Series (1997) (0)
Some Nonlinear Identities for Divisor Functions (2013) (0)
An Introduction to Sieve Methods and Their Applications: Some basic notions (2005) (0)
Dirichlet L-Functions (1997) (0)
Elementary Number Theory (1999) (0)
Non-vanishing of -functions (1997) (0)
THE ART OF RESEARCH (2017) (0)
Counting Finite Groups (1996) (0)
On a paper of S S Pillai (2012) (0)
Periods and Quasiperiods (2014) (0)
Periods, Multiple Zeta Functions and ζ (3) (2014) (0)
More Elliptic Integrals (2014) (0)
Overview of the Work of Kumar Murty (2016) (0)
The Structure of Units (1999) (0)
Möbius Inversion and Graph Colouring (2009) (0)
A COMBINATORIAL IDENTITY FOR STUDYING SATO-TATE TYPE PROBLEMS (2010) (0)
L-Series and Transcendental Numbers (2011) (0)
The Ramanujan Conjecture from GL(2) to GL(n) (2013) (0)
The Principle of Inclusion and Exclusion (2009) (0)
Smooth arithmetical sums over k-free integers (2019) (0)
An Introduction to Sieve Methods and Their Applications: Brun's sieve (2005) (0)
SOME RECENT DEVELOPMENTS IN NUMBER THEORY (2017) (0)
Equidistribution and L-Functions (1997) (0)
The Schneider–Lang Theorem (2014) (0)
Review of "Indian Philosophy in English: From Renaissance to Independence" (2014) (0)

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Published Works

What Schools Are Affiliated With Maruti Ram Murty?

Maruti Ram Murty's AcademicInfluence.com Rankings