Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations
Number Theory
2013-12-05 v1 Mathematical Physics
math.MP
Abstract
The classical transformation of Jacobi's theta function admits a simple proof by producing an integral representation that yields this invariance apparent. This idea seems to have first appeared in the work of S. Ramanujan. Several examples of this idea have been produced by Koshlyakov, Ferrar, Guinand, Ramanujan and others. A unifying procedure to analyze these examples and natural generalizations is presented.
Cite
@article{arxiv.1312.1232,
title = {Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations},
author = {Atul Dixit and Victor H. Moll},
journal= {arXiv preprint arXiv:1312.1232},
year = {2013}
}
Comments
34 pages; submitted for publication