Phantom holomorphic projections arising from Sturm's formula
Number Theory
2016-05-09 v1
Abstract
We show the analytic continuation of certain Siegel Poincar\'e series to their critical point for weight three in genus two. We proof that this continuation posesses a nonhomomorphic part and describe it. We show that Sturm's operator also produces a nonhomorphic share for weight three, we call it a phantom term. Weight three is the distinguished weight for genus two where this phenomenon arises.
Cite
@article{arxiv.1605.01868,
title = {Phantom holomorphic projections arising from Sturm's formula},
author = {Kathrin Maurischat and Rainer Weissauer},
journal= {arXiv preprint arXiv:1605.01868},
year = {2016}
}