English

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}
}
R2 v1 2026-06-22T13:54:36.800Z