We prove that all mod *p^m* singular forms of level *N*, degree *n+r*, and *p*-rank *r* with *n\ge r* are congruent mod *p^m* to linear combinations of theta series of degree *r* attached to quadratic forms of some level. Moreover, we prove that, the levels of theta series are of... Show more

February 1, 2023

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Structure theorem for mod $p^m$ singular Siegel modular forms

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