Philadelphia Area Number Theory Seminar

Wednesday, April 25, 2018 - 2:15pm

Alexander Jason Dunn

University of Illinois at Urbana-Champaign

In 2015, Vaughn obtained asymptotic formulas for the number of partitions of an integer into squares. Gafni extended this to kth powers. Here we obtain such formulas for the number of partitions into values of an arbitrary integer polynomial f subject to some mild hypotheses. Our methods use an interplay of the circle method, the polylogarithm, and the Matsumoto–Weng zeta function. This is joint work with Nicolas Robles.