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Number Theory Seminar

Arithmetic statistics of modular symbols

Yiannis Petridis (University College London)

Location:  Zoom
Date & time: Tuesday, 27 April 2021 at 2:00PM - 3:00PM

Abstract: The central value of the L-function of an elliptic curve has been the object of extensive studies in the last 50 years. Associated with such a curve we wish to understand also families of twists of it, leading to the study of twisted L-functions. On the other hand modular symbols have been a useful tool to study the space of holomorphic cusp forms of weight 2, and the homology of modular curves. They have been the object of extensive investigations by many mathematicians including Birch, Manin, and Cremona. Mazur, Rubin, and Stein have recently formulated a series of conjectures about statistical properties of modular symbols in order to understand central values of twists of elliptic curve L-functions. We discuss some of these conjectures and the recent progress and resolution of them. This is joint work with M. S. Risager.

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