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

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Year 2010
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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.
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KARLSSON, Anders. Applications of heat kernels on abelian groups: ζ(2n), quadratic reciprocity, Bessel integrals. 2010. https://archive-ouverte.unige.ch/unige:17265

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Deposited on : 2011-10-31

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