William Stein, U.C. Berkeley

``Period Integrals of Newforms''

May 5, 1999

Let $f(z)$ be a newform of even weight $k$. We can numerically approximate the integral along the path from 0 to infinity of $f(z)z^j dz$, using a change of variable trick. In this talk I will describe some of the interesting relations which arise, and then give examples of $j$-invariants of elliptic curves attached to higher weight rational newforms, e.g., Ramanujan's $\Delta$ function.


ERRATA: Last week I incorrectly asserted that the period ratios for j odd are 0. In fact only their real parts must be 0, as they are pure imaginary.