### A double sum of Jacobi symbols and multiple Dirichlet series

Linfoot Number Theory Seminar

26th May 2021, 11:00 am – 12:00 pm

Fry Building, Online

We will study the double sum of Jacobi symbols

\sum_{n\leq X}\sum_{m\leq Y}\left(\frac{m}{n}\right).

This sum was studied by Conrey, Farmer, and Soundararajan, who gave a surprising asymptotic formula. We will show how to obtain the same asymptotic with an improved error term by transforming the double sum into a double integral that involves a double Dirichlet series, and study the analytic properties of the double Dirichlet series.

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