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Hecke $L$-Functions and the Distribution of Totally Positive Integers

Published online by Cambridge University Press:  20 November 2018

Avner Ash  and
Solomon Friedberg
Avner Ash
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, U.S.A. email: ashav@bc.edu, friedber@bc.edu
Solomon Friedberg
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, U.S.A. email: ashav@bc.edu, friedber@bc.edu
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Abstract

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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.

Keywords

11M4111F3011F5511H0611R47Eisenstein seriestoroidal integralFourier seriesHecke L-functiontotally positive integertrace
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 4 , 01 August 2007 , pp. 673 - 695
Copyright
Copyright © Canadian Mathematical Society 2007

References

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