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Submitted by sde on 11 August, 2016 - 23:25

Date/Time:

Thursday, August 25, 2016 - 04:35 to 05:30

Venue:

SMS seminar Hall

Speaker:

Srilakshmi Krishnamoorthy

Affiliation:

Indian Institute of Technology Chennai

Title:

ON THE FOURIER COEFFICIENTS OF A COHEN-EISENSTEIN SERIES

In the first part of this talk, we present a formula for the coefficients of a weight 3/2Cohen-Eisenstein series of squarefree level N. This formula generalizes a result of Gross and it provesin particular a conjecture of Quattrini. In the second part, we explain the proof of this formula andas an application, we discuss the distribution of the order of the Tate-Shafarevich groups #ShD ofquadratic twists of elliptic curves.

**School of Mathematical Sciences**

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