1. CJM 2007 (vol 59 pp. 673)
|Hecke $L$-Functions and the Distribution of Totally Positive Integers |
Let $K$ be a totally real number field of degree $n$. We show that the number of totally positive integers (or more generally the number of totally positive elements of a given fractional ideal) of given trace is evenly distributed around its expected value, which is obtained from geometric considerations. This result depends on unfolding an integral over a compact torus.
Keywords:Eisenstein series, toroidal integral, Fourier series, Hecke $L$-function, totally positive integer, trace
Categories:11M41, 11F30, , 11F55, 11H06, 11R47
2. CJM 2003 (vol 55 pp. 933)
|Renormalized Periods on $\GL(3)$ |
A theory of renormalization of divergent integrals over torus periods on $\GL(3)$ is given, based on a relative truncation. It is shown that the renormalized periods of Eisenstein series have unexpected functional equations.