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arXiv · 1605.01868

Phantom holomorphic projections arising from Sturm's formula

Kathrin Maurischat·Rainer Weissauer
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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.

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Kathrin Maurischat, Rainer Weissauer. 2016-05-06. Phantom holomorphic projections arising from Sturm's formula. https://arxiv.org/abs/1605.01868

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