16 citations · 40 across the 20 of their papers we have counts for
23 papers
Modular Functions and the Monstrous Exponents
John F. R. Duncan, Holly Swisher
We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple…
Repellent properties of perfect powers on partition functions: a heuristic approach
Summer Haag, Praneel Samanta, Swati +3
In 2013, Sun conjectured that the partition function is never a perfect power for . Building on this, Merca, Ono, and Tsai recently observed that for any fixed int…
Generalized Alder-Type Partition Inequalities
Liam Armstrong, Bryan Ducasse, Thomas Meyer +1
In 2020, Kang and Park conjectured a "level " Alder-type partition inequality which encompasses the second Rogers-Ramanujan Identity. Duncan, Khunger, the fourth author, and Tam…
Generalized Ramanujan-Sato Series Arising from Modular Forms
Angelica Babei, Lea Beneish, Manami Roy +3
Motivated by work of Chan, Chan, and Liu, we obtain a new general theorem which produces Ramanujan-Sato series for . We then use it to construct explicit examples related to n…
Generalizations of Alder's Conjecture via a Conjecture of Kang and Park
Adriana L. Duncan, Simran Khunger, Holly Swisher +1
Integer partitions have long been of interest to number theorists, perhaps most notably Ramanujan, and are related to many areas of mathematics including combinatorics, modular for…
An analogue of -marked Durfee symbols for strongly unimodal sequences
Savana Ammons, Young Jin Kim, Laura Seaberg +1
In a seminal 2007 paper, Andrews introduced a class of combinatorial objects that generalize partitions called -marked Durfee symbols. Multivariate rank generating functions for…
Inequalities for the th Residual Crank Moments of Overpartitions
Ali H. Al-Saedi, Thomas Morrill, Holly Swisher
Two analogues of the crank function are defined for overpartitions -- the first residual crank and the second residual crank. This suggests an exploration of crank functions define…
Extending a catalog of mock and quantum modular forms to an infinite class
Allison Arnold-Roksandich, Brian Diaz, Erin Ellefsen +1
Utilizing a classification due to Lemke Oliver of eta-quotients which are also theta functions (here called eta-theta functions), Folsom, Garthwaite, Kang, Treneer, and the fourth…
Quantum modular forms and singular combinatorial series with repeated roots of unity
Amanda Folsom, Min-Joo Jang, Sam Kimport +1
In 2007, G.E. Andrews introduced the -variable combinatorial generating function for ranks of -marked Durfee symbols, an -dimensional m…
Eta-quotients of Prime or Semiprime Level and Elliptic Curves
Michael Allen, Nicholas Anderson, Asimina Hamakiotes +2
From the Modularity Theorem proven by Wiles, Taylor, et al, we know that all elliptic curves are modular. It has been shown by Martin and Ono exactly which are represented by eta-q…
Quantum modular forms and singular combinatorial series with distinct roots of unity
Amanda Folsom, Min-Joo Jang, Sam Kimport +1
Understanding the relationship between mock modular forms and quantum modular forms is a problem of current interest. Both mock and quantum modular forms exhibit modular-like trans…
Mock modularity of the -rank of overpartitions
Chris Jennings-Shaffer, Holly Swisher
We investigate the modular properties of a new partition rank, the -rank of overpartitions. In fact this is an infinite family of ranks, indexed by the positive integer , t…
A Cubic Transformation Formula for Appell-Lauricella Hypergeometric Functions over Finite Fields
Sharon Frechette, Holly Swisher, Fang-Ting Tu
We define a finite-field version of Appell-Lauricella hypergeometric functions built from period functions in several variables, paralleling the development by Fuselier, et. al in…
Quantum mock modular forms arising from eta-theta functions
Amanda Folsom, Sharon Garthwaite, Soon-Yi Kang +2
In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta-theta functions by constructing mock modular forms from the eta-theta…
Extension of a proof of the Ramanujan congruences for multipartitions
Oleg Lazarev, Matthew S. Mizuhara, Benjamin Reid +1
Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function . Their proof uses only the classical theory of m…
Hypergeometric Functions over Finite Fields
Jenny Fuselier, Ling Long, Ravi Ramakrishna +2
Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type alge…
A proof of some conjectures of Mao on partition rank inequalities
Ethan Alwaise, Elena Iannuzzi, Holly Swisher
Based on work of Atkin and Swinnerton-Dyer on partition rank difference functions, and more recent work of Lovejoy and Osburn, Mao has proved several inequalities between partition…
A periodic approach to plane partition congruences
Matthew S. Mizuhara, James A. Sellers, Holly Swisher
Ramanujan's celebrated congruences of the partition function have inspired a vast amount of results on various partition functions. Kwong's work on periodicity of rational p…
On the supercongruence conjectures of van Hamme
Holly Swisher
In 1997, van Hamme developed adic analogs, for primes , of several series which relate hypergeometric series to values of the gamma function, originally studied by Ramanujan…
Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions
Alyson Deines, Jenny G. Fuselier, Ling Long +2
In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hyperg…
Generalized Legendre curves and Quaternionic Multiplication
Alyson Deines, Jenny G. Fuselier, Ling Long +2
This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphis…
On a conjecture of Kimoto and Wakayama
Ling Long, Robert Osburn, Holly Swisher
We prove a conjecture due to Kimoto and Wakayama from 2006 concerning Apery-like numbers associated to a special value of a spectral zeta function. Our proof uses hypergeometric se…
Zeros of some level 2 Eisenstein series
Sharon Garthwaite, Ling Long, Holly Swisher +1
The zeros of classical Eisenstein series satisfy many intriguing properties. Work of F. Rankin and Swinnerton-Dyer pinpoints their location to a certain arc of the fundamental doma…