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