p-Adic Variation and Modular Forms


Glenn Stevens

Boston University

Brandeis University

Thursday, September 12, 2002


Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall


Abstract:   Modular forms are complex analytic objects that encode arithmetic data coming from elliptic curves and other arithmetic geometric sources. It is also possible to do arithmetic with the modular forms themselves and this has important consequences for the arithmetic data they encode. By looking at concrete examples, I will discuss the evolution of the concept of congruences and p-adic variation of modular forms and will describe some of the many consequences for the theory of L-functions. In particular, I will explain briefly how p-adic L-functions vary over the Coleman-Mazur eigencurve and describe recent numerical experiments with Robert Pollack that produce new examples of p-adic L-functions. The lecture will be aimed at graduate students and non-specialists except for a few remarks near the end.

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