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The Sato-Tate conjecture for modular forms

Martin Dickson

Pure Postgraduate Seminar

Organisers: Andrew Poulton, Henry Reeve

ABSTRACT
Have you ever noticed that "Sato-Tate" rhymes with "great"?  This is a coincidence.  That the Hecke eigenvalues of modular forms are equidistributed with respect to Sato-Tate measure is, however, not.  In this talk I'll introduce the original Sato-Tate conjecture for elliptic curves, explain how this naturally generalises to a conjecture about modular forms, and give an example of an arithmetic application of the latter.