2017, American Mathematical Society Colloquium Publications, ISBN 9781470419448, Volume 64., xv, 391 pages

Book

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, ISSN 0027-8424, 06/2019, Volume 116, Issue 23, pp. 11103 - 11110

In 1927, Polya proved that the Riemann hypothesis is equivalent to the hyperbolicity of Jensen polynomials for the Riemann zeta function zeta(s) at its point...

TURAN | Jensen polynomials | Riemann hypothesis | hyperbolic polynomials | MULTIDISCIPLINARY SCIENCES | Partitions (mathematics) | Theorems | Sequences | Hermite polynomials | Physical Sciences

TURAN | Jensen polynomials | Riemann hypothesis | hyperbolic polynomials | MULTIDISCIPLINARY SCIENCES | Partitions (mathematics) | Theorems | Sequences | Hermite polynomials | Physical Sciences

Journal Article

Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 4/2013, Volume 110, Issue 15, pp. 5765 - 5768

In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. Recent work by Zwegers [Zwegers...

Integers | Series convergence | Mathematical theorems | Infinity | Fourier series expansion | Mathematical functions | Coefficients | Combinatorics | Fourier coefficients | Modular form | Harmonic maass form | Radial limits | modular form | radial limits | harmonic Maass form | MULTIDISCIPLINARY SCIENCES | Physical Sciences

Integers | Series convergence | Mathematical theorems | Infinity | Fourier series expansion | Mathematical functions | Coefficients | Combinatorics | Fourier coefficients | Modular form | Harmonic maass form | Radial limits | modular form | radial limits | harmonic Maass form | MULTIDISCIPLINARY SCIENCES | Physical Sciences

Journal Article

Research in the Mathematical Sciences, ISSN 2522-0144, 12/2015, Volume 2, Issue 1, pp. 1 - 18

Inspired by the original definition of mock theta functions by Ramanujan, a number of authors have considered the question of explicitly determining their behavior at the cusps...

Mathematics, general | Computational Mathematics and Numerical Analysis | Mathematics | Applications of Mathematics | MATHEMATICS

Mathematics, general | Computational Mathematics and Numerical Analysis | Mathematics | Applications of Mathematics | MATHEMATICS

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2018, Volume 329, pp. 541 - 554

The denominator formula for the Monster Lie algebra is the product expansion for the modular function J(z)−J(τ) given in terms of the Hecke system of...

Divisors of modular forms | Denominator formula | Polar harmonic Maass forms | MATHEMATICS | COEFFICIENTS | MOONSHINE

Divisors of modular forms | Denominator formula | Polar harmonic Maass forms | MATHEMATICS | COEFFICIENTS | MOONSHINE

Journal Article

Research in the mathematical sciences, ISSN 2197-9847, 2018, Volume 5, Issue 1, pp. 1 - 15

... of polynomials
Nikolaos Diamantis 1* and Larry Rolen 2
* Correspondence:
nikolaos.diamantis@nottingham.ac.uk 1
University of Nottingham,
Nottingham, UK
Full list of author...

Computational Mathematics and Numerical Analysis | Derivatives of L -functions | Eichler cohomology | Mathematics, general | Mathematics | Applications of Mathematics | Periods of modular forms | Critical L -values | 11F67 | 11F11 | Derivatives of L-functions | Critical L-values | MATHEMATICS | SPECIAL VALUES | UNIMODULARITY | MODULAR-FORMS

Computational Mathematics and Numerical Analysis | Derivatives of L -functions | Eichler cohomology | Mathematics, general | Mathematics | Applications of Mathematics | Periods of modular forms | Critical L -values | 11F67 | 11F11 | Derivatives of L-functions | Critical L-values | MATHEMATICS | SPECIAL VALUES | UNIMODULARITY | MODULAR-FORMS

Journal Article

Research in the mathematical sciences, ISSN 2197-9847, 2018, Volume 5, Issue 4, pp. 1 - 22

... , Ken Ono 2 and Larry Rolen 3*
* Correspondence:
larry.rolen@vanderbilt.edu 3
Department of Mathematics,
Vanderbilt University, 1326
Stevenson Center, Nashville, TN...

String theory | 11R29 | Computational Mathematics and Numerical Analysis | Black holes | 83C57 | Mathematics, general | Mathematics | Class numbers | Applications of Mathematics | 11E41 | FORMS | MATHEMATICS | ATTRACTORS | IMAGINARY QUADRATIC FIELDS | CURVES | CLASS-NUMBERS | ELLIPTIC GENERA | ENTROPY

String theory | 11R29 | Computational Mathematics and Numerical Analysis | Black holes | 83C57 | Mathematics, general | Mathematics | Class numbers | Applications of Mathematics | 11E41 | FORMS | MATHEMATICS | ATTRACTORS | IMAGINARY QUADRATIC FIELDS | CURVES | CLASS-NUMBERS | ELLIPTIC GENERA | ENTROPY

Journal Article

Forum Mathematicum, ISSN 0933-7741, 03/2015, Volume 27, Issue 2, pp. 961 - 972

In a recent paper, Bruinier and Ono prove that the coefficients of certain weight
harmonic Maass forms are traces of singular moduli for weak Maass forms. In...

Singular moduli | Maass forms | 11P99 | 11F37 | partition function | MATHEMATICS | MATHEMATICS, APPLIED

Singular moduli | Maass forms | 11P99 | 11F37 | partition function | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Research in the Mathematical Sciences, ISSN 2522-0144, 12/2014, Volume 1, Issue 1, pp. 1 - 17

.... Since then, a number of authors have proven refined results, for example, extending all of these congruences to arbitrary powers of the primes involved...

Mathematics, general | Computational Mathematics and Numerical Analysis | Mathematics | Applications of Mathematics | DIAGRAMS | MATHEMATICS | VALUES | IDENTITIES | Q-SERIES

Mathematics, general | Computational Mathematics and Numerical Analysis | Mathematics | Applications of Mathematics | DIAGRAMS | MATHEMATICS | VALUES | IDENTITIES | Q-SERIES

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 12/2011, Volume 7, Issue 8, pp. 2237 - 2247

We study a certain generalization of the classical Congruent Number Problem. Specifically, we study integer areas of rational triangles with an arbitrary fixed...

FORMS | MATHEMATICS | Congruent number problem | arithmetic statistics | CURVES | parity conjecture

FORMS | MATHEMATICS | Congruent number problem | arithmetic statistics | CURVES | parity conjecture

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2016, Volume 144, Issue 4, pp. 1453 - 1456

.... This theorem has begun to play an important role in the theory of harmonic Maass forms, and was crucial to work of Guerzhoy as well as Alfes, Griffin, Ono, and the author...

MATHEMATICS | MATHEMATICS, APPLIED

MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 05/2020, Volume 120, Issue 5, pp. 742 - 769

Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of L‐functions. In particular, we find a...

11M20 (primary) | 11F37 | 11E76 | 11F11 | MATHEMATICS | FOURIER COEFFICIENTS | MODULAR-FORMS | CONJECTURE

11M20 (primary) | 11F37 | 11E76 | 11F11 | MATHEMATICS | FOURIER COEFFICIENTS | MODULAR-FORMS | CONJECTURE

Journal Article

09/2020

Recently, Mertens, Ono, and the third author studied mock modular analogues
of Eisenstein series...

Mathematics - Number Theory

Mathematics - Number Theory

Journal Article

04/2015

...) completion of this
form which is doubly periodic. This theorem has begun to play an important role
in the theory of harmonic Maass forms, and was crucial to work of Guerzhoy as
well as Alfes, Griffin, Ono, and the author...

Mathematics - Number Theory

Mathematics - Number Theory

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2017, Volume 145, Issue 2, pp. 543 - 557

In this paper, we answer a question of Li, Ngo, and Rhoades concerning a set of q-series related to the q-hypergeometric series \sigma from Ramanujan's Lost...

MATHEMATICS | MATHEMATICS, APPLIED

MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 2/2012, Volume 27, Issue 2, pp. 151 - 162

... · Jeffrey Beyerl · Jim Brown ·
Allison Proffer · Larry Rolen
Received: 24 September 2010 / Accepted: 13 April 2011 / Published online: 3 August 2011
© Springer Science...

11F46 | Fourier Analysis | Functions of a Complex Variable | Special values of L -functions | Field Theory and Polynomials | Mathematics | 11F30 | Number Theory | Combinatorics | Pullbacks of Eisenstein series | 11F67 | Special values of L-functions | MATHEMATICS | Universities and colleges

11F46 | Fourier Analysis | Functions of a Complex Variable | Special values of L -functions | Field Theory and Polynomials | Mathematics | 11F30 | Number Theory | Combinatorics | Pullbacks of Eisenstein series | 11F67 | Special values of L-functions | MATHEMATICS | Universities and colleges

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 01/2017, Volume 306, pp. 328 - 343

Answering problems of Manin, we use the critical L-values of even weight k≥4 newforms f∈Sk(Γ0(N)) to define zeta-polynomials Zf(s) which satisfy the functional...

Period polynomials | Zeta-polynomials | Modular forms | Ehrhart polynomials | Bloch–Kato complex | MATHEMATICS | ROOTS | Bloch Kato complex | Computer science

Period polynomials | Zeta-polynomials | Modular forms | Ehrhart polynomials | Bloch–Kato complex | MATHEMATICS | ROOTS | Bloch Kato complex | Computer science

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 09/2018, Volume 2018, Issue 18, pp. 5537 - 5561

Abstract
Using special polynomials related to the Andrews–Gordon identities and the coloured Jones polynomial of torus knots, we construct classes of...

MATHEMATICS | IDENTITIES

MATHEMATICS | IDENTITIES

Journal Article

Journal of number theory, ISSN 0022-314X, 2016, Volume 161, pp. 240 - 254

In analogy with the classical theory of Eichler integrals for integral weight modular forms, Lawrence and Zagier considered examples of Eichler integrals of...

L-series | Eichler integral | Modular form | Half-integral weight | Radial limits | MATHEMATICS | SERIES | DERIVATIVES

L-series | Eichler integral | Modular form | Half-integral weight | Radial limits | MATHEMATICS | SERIES | DERIVATIVES

Journal Article

Research in the mathematical sciences, ISSN 2197-9847, 2016, Volume 3, Issue 1, pp. 1 - 9

.... This extends recent work of Creutzig and the first two authors for the special case of Kac–Wakimoto characters which occur naturally in Lie theory and yields, as easy corollaries, many important PDEs arising in combinatorics such as the famous rank...

Mathematics, general | Computational Mathematics and Numerical Analysis | Mathematics | Applications of Mathematics | Vertex Algebra | Vertex Operator Algebra | Modular Form | Fourier Coefficient | Jacobi Form | MATHEMATICS | CRANK-TYPE PDES | N-POINT FUNCTIONS | SUPERALGEBRAS | SERIES

Mathematics, general | Computational Mathematics and Numerical Analysis | Mathematics | Applications of Mathematics | Vertex Algebra | Vertex Operator Algebra | Modular Form | Fourier Coefficient | Jacobi Form | MATHEMATICS | CRANK-TYPE PDES | N-POINT FUNCTIONS | SUPERALGEBRAS | SERIES

Journal Article

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