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# Texas A&M Number Theory Seminar

##
Department of Mathematics

Blocker 220

Wednesdays, 1:45–2:45 PM

### Sheng-Chi Liu

Washington State University

#### Wednesday, February 12, 2020

#### Blocker 220, 1:45PM

**Title:** * A GL_3 Analog of Selberg's Result on S(t)
*

**Abstract:**
The function *S(t)* appears in an asymptotic formula for counting the number of nontrivial zeros of the Riemann zeta function with imaginary part less than *t*. It was shown by Littlewood that the function has a lot of cancellation on the average over *t*. Later Selberg studied the moments of *S(t)* and the moments of the analog function associated with a Dirichlet L-function for a primitive Dirichlet character. A GL_2 analog of Selberg's
result was proved by Hejhal and Luo. In this talk we will discuss a GL_3 analog of such results. This is joint work with Shenhui Liu.