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.