5 papers · 1 filter
Negative bias in moments of the Legendre family of elliptic curves
Ben Kane, Mikuláš Zindulka
We determine the bias in higher moments of the Legendre family of elliptic curves in view of the Negative Bias Conjecture of S. J. Miller. We show that every lower order term is ei…
A direct proof of Mono-Rolen-Stumpenhusen and new constructions via the Maass raising operators
Kathrin Bringmann, Ben Kane
In this paper, we give a direct conceptual proof of the main result of Mono, Rolen, and Stumpenhusen, using differential operators. More precisely, we realize their functions $Ï_{…
Strict Log-concavity of -coloured Partitions
Kathrin Bringmann, Ben Kane, Anubhab Pahari +1
In recent years, there has been extensive work on inequalities among partition functions. In particular, Nicolas, and independently DeSalvo--Pak, proved that the partition function…
A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences
Koustav Banerjee, Kathrin Bringmann, Ben Kane
We derive an asymptotic expansion with effective error bound for , counting the number of unimodal sequences of size . We prove that satisfies the higher order TurÃ…
The bias conjecture for elliptic curves over finite fields and Hurwitz class numbers in arithmetic progressions
Ben Kane, Sudhir Pujahari, Zichen Yang
In this paper, we consider a version of the bias conjecture for second moments in the setting of elliptic curves over finite fields whose trace of Frobenius lies in an arbitrary fi…