Galois action on special theta values
Number Theory
2014-09-26 v1
Abstract
Using Shimura's reciprocity law, we calculate the Galois action on the special values of theta functions associated to primitive Dirichlet characters of odd conductor, normalised by the Dedekind eta function, at the point i. As a consequence, we prove some experimental results of Cohen and Zagier and we deduce a partial result on the non-vanishing of these special theta values with prime conductor.
Cite
@article{arxiv.1409.7214,
title = {Galois action on special theta values},
author = {Paloma Bengoechea},
journal= {arXiv preprint arXiv:1409.7214},
year = {2014}
}
Comments
13 pages, To appear in Journal de Theorie des Nombres de Bordeaux