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Philadelphia Area Number Theory Seminar

Tuesday, October 18, 2022 - 2:30pm

Ellen Eischen

University of Oregon


Swarthmore College

Science Center, Room 149

Informal refreshments will be served at 2:00 p.m.

I will discuss recent developments and ongoing work for p-adic aspects of modular forms and L-functions, which encode arithmetic data. Interest in p-adic properties of values of L-functions originated with Kummer's study of congruences between values of the Riemann zeta function at negative odd integers, as part of his attempt to under- stand class numbers of cyclotomic extensions. After presenting an approach to proving congruences and constructing p-adic L-functions, I will conclude the talk by introduc- ing ongoing joint work of G. Rosso, S. Shah, and myself (concerning Spin L-functions for GSp 6). I will explain how this work  t into the context of earlier developments, including constructions of Serre, Katz, Coates{Sinnot, Deligne{Ribet, Hida, E{Harris{ Li{Skinner, and Liu. I will not assume the audience has prior familiarity with p-adic L-functions or Spin L-functions, and all who are curious about this topic are welcome.