4 papers
Quasimodular Forms, Partitions, and Primes in Intervals
Kevin Allen, William Craig
Recent developments in theories of partitions, quasimodular forms, multiple zeta values and -multiple zeta values have led to connections between partitions and primes. Central…
Generalized rank deviations for overpartitions
Kevin Allen, Robert Osburn, Matthias Storzer
We prove formulas for generalized rank deviations for overpartitions. These formulas are in terms of Appell-Lerch series and sums of quotients of theta functions and extend work of…
Unimodal sequences and mixed false theta functions
Kevin Allen, Robert Osburn
We consider two-parameter generalizations of Hecke-Appell type expansions for the generating functions of unimodal and special unimodal sequences. We then determine their explicit…
On Translation Hyperovals in Semifield Planes
Kevin Allen, John Sheekey
In this paper we demonstrate the first example of a finite translation plane which does not contain a translation hyperoval, disproving a conjecture of Cherowitzo. The counterexamp…