The search for padic automorphic forms
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Modular forms have been a central object of study in number theory for many years. In the 1970s, Serre introduced padic modular forms. These are more general objects which, unlike classical modular forms, live in padic families. Since then, the theory of padic modular forms has seen many applications to classical problems in number theory, especially in the Langlands program. Modular forms are special cases of more general objects: automorphic forms and automorphic representations. However, the concept of a “padic automorphic form” is more elusive. In this talk, I will explain the basics of the theory of (padic) modular forms, what properties we look for in the more general padic automorphic forms, and some of their proposed constructions.
This talk is part of the Junior Algebra and Number Theory seminar series.
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