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Allison Arnold-Roksandich

Publications and source records attributed to Allison Arnold-Roksandich.

3 recordsLinked to original sources
arXiv2019

Extending a catalog of mock and quantum modular forms to an infinite class

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 author constructed a catalog of mock modular forms $V_{mn}$ having weight $3/2$ eta-theta function shadows and showed that these mock modular forms when viewed on certain sets of rationals, transform as quantum modular forms under the action of explicit subgroups. In this paper, we introduce an infinite class of functions that generalizes one row of the catalog, namely the $V_{m1}$, and show that the functions in this infinite class are both mock modular and quantum modular forms.

math.NT↗
arXiv2018

Proceedings Paper for REU Project Involving Counting Eta-Quotients

It is known that all modular forms on $SL_2(Z)$ can be expressed as a rational function in $η(z)$, $η(2z)$ and $η(4z)$. By using a theorem by Gordon, Hughes, and Newman, and calculating the order of vanishing, we can compute the $η$-quotients for a given level. Using this count, knowing how many $η$-quotients are linearly independent and using the dimension formula, we can figure out how the $η$-quotients span higher levels. In this paper, we primarily focus on the case where $N=p$ a prime, and some discussion for non-prime indicies.

math.NT↗
arXiv2016

Counting Eta-Quotients of Prime Level

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 vanishing, we can compute the eta-quotients for a given level. Using this count, knowing how many eta-quotients are linearly independent and using the dimension formula, we can figure out a subspace spanned by the eta-quotients. In this paper, we primarily focus on the case where N=p a prime.

math.NT↗