Hermitian modular forms congruent to 1 modulo p

摘要

For any natural number l and any prime p≡ 1 (mod 4) not divid-ing is there is a Hermitian modular form of arbitrary genus n over L := Q[/] that is congruent to 1 modulo p which is a Hermitian theta series of an OL-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.