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Special Values of automorphic L-functions and congruences

Automorphic forms, Shimura varieties, Galois representations and L-functions December 01, 2014 - December 05, 2014

December 03, 2014 (09:00 AM PST - 10:00 AM PST)
Speaker(s): A. Raghuram (Indian Institute of Science Education and Research)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14113

Abstract

Hida proved in 1981 that if a prime p divides the algebraic part of the value at s = 1 of the adjoint L-function of a holomorphic cusp form f, then there is another cusp form g such that f is congruent to g modulo the prime p. This result was generalized to Hilbert modular forms by Eknath Ghate and Mladen Dimitrov, and to certain cusp forms on GL(2) over an imaginary quadratic field by Eric Urban, and recently to cusp forms on GL(2) over any number field by Namikawa. In this talk, I will discuss further generalizations of this phenomenon to the context adjoint L-values for cohomological cuspidal automorphic representations of GL(n) over any number field. This is joint work with Baskar Balasubramanyam

Supplements
22426?type=thumb Notes Raghuram 268 KB application/pdf Download
Video/Audio Files

14113

H.264 Video 14113.mp4 331 MB video/mp4 rtsp://videos.msri.org/data/000/022/323/original/14113.mp4 Download
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