4 papers · 1 filter
Representations of integers as sums of four polygonal numbers and partial theta functions
Kathrin Bringmann, Min-Joo Jang, Ben Kane +1
In this paper, we consider representations of integers as sums of at most four distinct -gonal numbers (allowing a fixed number of repeats of each polygonal number occurring in…
A modular framework for functions of Knopp and indefinite binary quadratic forms
Kathrin Bringmann, Andreas Mono
We study functions introduced by Knopp and complete them to non-holomorphic bimodular forms of positive integral weight related to indefinite binary quadratic forms. We investigate…
Flipping operators and locally harmonic Maass forms
Kathrin Bringmann, Andreas Mono, Larry Rolen
In the theory of integral weight harmonic Maass forms of manageable growth, two key differential operators, the Bol operator and the shadow operator, play a fundamental role. Harmo…
Odd moments for the trace of Frobenius and the Sato--Tate conjecture in arithmetic progressions
Kathrin Bringmann, Ben Kane, Sudhir Pujahari
In this paper, we consider the moments of the trace of Frobenius of elliptic curves if the trace is restricted to a fixed arithmetic progression. We determine the asymptotic behavi…