Even powers of divisors and elliptic zeta values

Details Even powers of divisors and elliptic zeta values Even powers of divisors and elliptic zeta values

2002-05-10

arxiv.org/abs/math/0205116v2

J. Reine Angew. Math. 579 (2005), 195--201

Mathematics

Quantum Algebra

5 pages. Final version, with an alternative proof of the main result by Don Zagier

Scientific paper

10.1515/crll.2005.2005.579.195

We introduce and study "elliptic zeta values", a two-parameter deformation of the values of Riemann's zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share the SL(3,Z) modular properties of this function. Elliptic zeta values at even integers are related to Eisenstein series and thus to sums of odd powers of divisors. The elliptic zeta values at odd integers can be expressed in terms of generating series of sums of even powers of divisors.

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