18 citations · 51 across the 6 of their papers we have counts for
6 papers
Proceedings Paper for REU Project Involving Counting Eta-Quotients
Allison Arnold-Roksandich, Kevin James, Rodney Keaton
It is known that all modular forms on can be expressed as a rational function in , and . By using a theorem by Gordon, Hughes, and Newman, and calcul…
Counting Eta-Quotients of Prime Level
Allison Arnold-Roksandich, Kevin James, Rodney Keaton
It is known that all modular forms on SL_2(Z) can be expressed as a rational function in eta(z), eta(2z) and eta(4z). By utilizing known theorems, and calculating the order of vani…
Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals
Kevin James, Ethan Smith
Let be a fixed number field, assumed to be Galois over . Let and be fixed integers with positive. Given an elliptic curve , defined over , we consi…
Finite field elements of high order arising from modular curves
Jessica F. Burkhart, Neil J. Calkin, Shuhong Gao +6
In this paper, we recursively construct explicit elements of provably high order in finite fields. We do this using the recursive formulas developed by Elkies to describe explicit…
Elliptic curves, modular forms, and sums of Hurwitz class numbers
Brittany Brown, Neil J. Calkin, Timothy B. Flowers +3
Let H(N) denote the Hurwitz class number. It is known that if is a prime, then {equation*} \sum_{|r|<2\sqrt p}H(4p-r^2) = 2p. {equation*} In this paper, we investigate the beha…
Products of Nearly Holomorphic Eigenforms
Jeffrey Beyerl, Kevin James, Catherine Trentacoste +1
We prove that the product of two nearly holomorphic Hecke eigenforms is again a Hecke eigenform for only finitely many choices of factors.