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arXiv · 0810.5310

Hermitian modular forms congruent to 1 modulo p

Michael Hentschel·Gabriele Nebe
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Abstract

For any natural number $\ell $ and any prime $p\equiv 1 \pmod{4}$ not dividing $\ell $ there is a Hermitian modular form of arbitrary genus $n$ over $L:=\Q [\sqrt{-\ell}]$ that is congruent to 1 modulo $p$ which is a Hermitian theta series of an $O_L$-lattice of rank $p-1$ admitting a fixed point free automorphism of order $p$. It is shown that also for non-free lattices such theta series are modular forms.

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Michael Hentschel, Gabriele Nebe. 2008-10-29. Hermitian modular forms congruent to 1 modulo p. https://arxiv.org/abs/0810.5310

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