Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Number Theory Seminar


Wednesday, July 31st, 2019

Time: 3:30-4:30 p.m.  Place: Jeffery Hall 319

Speaker: Akshaa Vatwani (IIT Gandhinagar)

Title: The Voronoi Summation Formula for a generalized divisor function.

Abstract: In 1904, Vorono\" {\i} formulated a conjecture for arithmetical functions, which is a generalization of the Poisson summation formula. He was able to establish this conjecture for the divisor function $d(n)$, giving a relation between Bessel functions and weighted sums of the divisor function. Such formulas have since been generalized to various arithmetical functions. We report on joint work with Atul Dixit, Bibekananda Maji and A. Sankaranarayanan, giving such a formula for the generalized divisor function:
$$
\sigma_{k,z} (n) = \sum_{d^k |n }d^z, \qquad \qquad k\in \mathbb N, \, z\in \mathbb{C}.
$$