Identities for the Ramanujan zeta function

Mathew Rogers

Identities for the Ramanujan zeta function

Number Theory 2013-04-17 v2 Classical Analysis and ODEs

Authors: Mathew Rogers

Abstract

We prove formulas for special values of the Ramanujan tau zeta function. Our formulas show that $L(\Delta, k)$ is a period in the sense of Kontsevich and Zagier when $k\ge12$ . As an illustration, we reduce $L(\Delta, k)$ to explicit integrals of hypergeometric and algebraic functions when $k\in\{12,13,14,15\}$ .

Keywords

zeta values and euler sums ramanujan identities and series zeta functions

Cite

@article{arxiv.1210.1942,
  title  = {Identities for the Ramanujan zeta function},
  author = {Mathew Rogers},
  journal= {arXiv preprint arXiv:1210.1942},
  year   = {2013}
}

Comments

10 pages

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