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1 results

Hecke $L$-Functions and the Distribution of Totally Positive Integers
Avner Ash, Solomon Friedberg
Journal:

Canadian Journal of Mathematics / Volume 59 / Issue 4 / 01 August 2007

Published online by Cambridge University Press:

20 November 2018, pp. 673-695

Print publication:

01 August 2007
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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.