Applications of heat kernels on abelian groups: ζ(2n), quadratic reciprocity, Bessel integrals

Karlsson, Anders

doi:10.1007/978-1-4614-1260-1_14

Preprint

English

Applications of heat kernels on abelian groups: ζ(2n), quadratic reciprocity, Bessel integrals

ContributorsKarlsson, Anders

Number of pages13

Publication date2010

Abstract

The discussion centers around three applications of heat kernel consid- erations on R, Z and their quotients. These are Euler's formula for ζ(2n), Gauss' quadratic reciprocity law, and the evaluation of certain integrals of Bessel functions. Some further applications are mentioned, including the functional equation of Rie- mann's ζ-function, the reflection formula for the Γ-function, and certain infinite sums of Bessel functions.

Affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

KARLSSON, Anders. Applications of heat kernels on abelian groups: ζ(2n), quadratic reciprocity, Bessel integrals. 2010, p. 13. doi: 10.1007/978-1-4614-1260-1_14

Preprint

Identifiers

PID : unige:17265
DOI : 10.1007/978-1-4614-1260-1_14

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Applications of heat kernels on abelian groups: ζ(2n), quadratic reciprocity, Bessel integrals

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