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math.NT2026
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…
math.NT2025
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…
math.NT2024
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…