Alexandru Popa : Rational decomposition of modular forms

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

March 4, 2009, 4 p.m.

In

SEO 427

Abstract

In a 1984 paper, Kohnen and Zagier developed the theory of modular forms with rational periods for the full modular group. I recall some of this theory, and present a new result decomposing an arbitrary cusp form into forms with rational even (or odd) periods. As a consequence, I discuss a decomposition of Hecke eigenforms in terms of forms with rational Fourier coefficients, given by Rankin-Cohen brackets of Eisenstein series.