P. Jenkins

activity

20092020

most citedBounds for coefficients of cusp forms and extremal lattices

15 citations · 34 across the 14 of their papers we have counts for

collaborators

18 papers

math.NT2020

The arithmetic of modular grids

Michael Griffin, Paul Jenkins, Grant Molnar

A modular grid is a pair of sequences $(f_{m})_{m}$ and $(g_{n})_{n}$ of weakly holomorphic modular forms such that for almost all $m$ and $n$ , the coefficient of $q^{n}$ in $f_{m}$ is the neg…

math.NT2020

Congruences for coefficients of modular functions in levels 3, 5, and 7 with poles at 0

Paul Jenkins, Ryan Keck

We give congruences modulo powers of $p \in {3, 5, 7}$ for the Fourier coefficients of certain modular functions in level $p$ with poles only at 0, answering a question posed by A…

math.NT2017★ 1 cited

Divisibility properties of coefficients of modular functions in genus zero levels

Victoria Iba, Paul Jenkins, Merrill Warnick

We prove divisibility results for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight $0$ and levels $6, 10, 12, 18$ w…

math.NT2017

Congruences for coefficients of level 2 modular functions with poles at 0

Paul Jenkins, Ryan Keck, Eric Moss

We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and the first…

math.NT2017

Zagier duality for level $p$ weakly holomorphic modular forms

Paul Jenkins, Grant Molnar

We prove Zagier duality between the Fourier coefficients of canonical bases for spaces of weakly holomorphic modular forms of prime level $p$ with $11 \leq p \leq 37$ with poles on…

math.NT2017

Differential operators on polar harmonic Maass forms and elliptic duality

Kathrin Bringmann, Paul Jenkins, Ben Kane

In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincaré series which span the space of such forms and show that the…

math.NT2017★ 6 cited

Weakly holomorphic modular forms in prime power levels of genus zero

Paul Jenkins, DJ Thornton

Let $M_{k}^{♯} (N)$ be the space of weight $k$ , level $N$ weakly holomorphic modular forms with poles only at the cusp at $\infty$ . We explicitly construct a canonical basis for $M…

math.NT2016

Zeros of modular forms of half integral weight

Amanda Folsom, Paul Jenkins

We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in $Z + \frac{1}{2}$ and show that almost all modular forms in these bases hav…

math.NT2014★ 1 cited

Coefficient Bounds for Level 2 Cusp Forms and Modular Functions

Paul Jenkins, Kyle Pratt

We give explicit upper bounds for the coefficients of arbitrary weight $k$ , level 2 cusp forms, making Deligne's well-known $O (n^{\frac{k - 1}{2} + ε})$ bound precise. We also derive a…

math.NT2014

Congruences for coefficients of modular functions

Paul Jenkins, DJ Thornton

We examine canonical bases for weakly holomorphic modular forms of weight $0$ and level $p = 2, 3, 5, 7, 13$ with poles only at the cusp at $\infty$ . We show that many of the Fouri…

math.NT2013

Interlacing of zeros of weakly holomorphic modular forms

Paul Jenkins, Kyle Pratt

We prove that the zeros of a family of extremal modular forms interlace, settling a question of Nozaki. Additionally, we show that the zeros of almost all forms in a basis for the…

math.NT2013★ 1 cited

Integral traces of weak Maass forms of genus zero odd prime level

Nathan Green, Paul Jenkins

Duke and the second author defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic…

math.NT2013

Zeros of weakly holomorphic modular forms of level 4

Andrew Haddock, Paul Jenkins

Let $M_{k}^{♯} (4)$ be the space of weakly holomorphic modular forms of weight $k$ and level $4$ that are holomorphic away from the cusp at $\infty$ . We define a canonical basis fo…

math.NT2012★ 4 cited

Zeros of weakly holomorphic modular forms of levels 2 and 3

Sharon Anne Garthwaite, Paul Jenkins

Let $M_{k}^{♯} (N)$ be the space of weakly holomorphic modular forms for $Γ_{0} (N)$ that are holomorphic at all cusps except possibly at $\infty$ . We study a canonical basis for $M_k…

math.NT2011

Divisibility Properties of Coefficients of Level $p$ Modular Functions for Genus Zero Primes

Nickolas Andersen, Paul Jenkins

Lehner's 1949 results on the $j$ -invariant showed high divisibility of the function's coefficients by the primes $p \in {2, 3, 5, 7}$ . Expanding his results, we examine a canonical ba…

math.NT2011★ 2 cited

Two-divisibility of the coefficients of certain weakly holomorphic modular forms

Darrin Doud, Paul Jenkins, John Lopez

We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier c…

math.NT2010★ 15 cited

Bounds for coefficients of cusp forms and extremal lattices

Paul Jenkins, Jeremy Rouse

A cusp form $f (z)$ of weight $k$ for $\SL_{2}(\Z)$ is determined uniquely by its first $ℓ := dim S_{k}$ Fourier coefficients. We derive an explicit bound on the $n$ th coefficie…

math.NT2009★ 4 cited

$p$ -adic properties of coefficients of weakly holomorphic modular forms

Darrin Doud, Paul Jenkins

We examine the Fourier coefficients of modular forms in a canonical basis for the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coe…

The arithmetic of modular grids

Congruences for coefficients of modular functions in levels 3, 5, and 7 with poles at 0

Divisibility properties of coefficients of modular functions in genus zero levels

Congruences for coefficients of level 2 modular functions with poles at 0

Zagier duality for level p weakly holomorphic modular forms

Differential operators on polar harmonic Maass forms and elliptic duality

Weakly holomorphic modular forms in prime power levels of genus zero

Zeros of modular forms of half integral weight

Coefficient Bounds for Level 2 Cusp Forms and Modular Functions

Congruences for coefficients of modular functions

Interlacing of zeros of weakly holomorphic modular forms

Integral traces of weak Maass forms of genus zero odd prime level

Zeros of weakly holomorphic modular forms of level 4

Zeros of weakly holomorphic modular forms of levels 2 and 3

Divisibility Properties of Coefficients of Level p Modular Functions for Genus Zero Primes

Two-divisibility of the coefficients of certain weakly holomorphic modular forms

Bounds for coefficients of cusp forms and extremal lattices

p-adic properties of coefficients of weakly holomorphic modular forms

Zagier duality for level $p$ weakly holomorphic modular forms

Divisibility Properties of Coefficients of Level $p$ Modular Functions for Genus Zero Primes

$p$ -adic properties of coefficients of weakly holomorphic modular forms