# On the transcendence of certain infinite series

## Algebra and Number Theory Seminar

## Meeting Details

For more information about this meeting, contact Allyson Borger, Kirsten Eisentraeger, Jack Huizenga, Mihran Papikian, Ae Ja Yee, John Lesieutre.

**Speaker:** Siddhi Pathak, PSU

**Abstract:** In 1737, Euler solved the Basel problem by evaluating the values of the Riemann zeta-function at even positive integers. He showed that $ \zeta(2k) $ is a rational multiple of $ \pi^{2k} $. Since then, there have been several generalizations of Euler's result. One such question is to evaluate and determine the arithmetic nature of the more general series, $ \sum_{n=1}^{\infty} A(n) / B(n) $, where $ A(X) $ and $ B(X) $ are suitable polynomials. Although it is possible to express these sums in terms of the polygamma functions, their arithmetic nature remains a mystery. In this talk, we will discuss analogs of this problem in two distinct scenarios.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 09/12/2019

**Time:** 11:00am - 11:50am