261 research outputs found
Vector valued formal Fourier-Jacobi series
H. Aoki showed that any symmetric formal Fourier-Jacobi series for the
symplectic group Sp_2(Z) is the Fourier-Jacobi expansion of a holomorphic
Siegel modular form. We prove an analogous result for vector valued symmetric
formal Fourier-Jacobi series, by combining Aoki's theorem with facts about
vector valued modular forms. Recently, this result was also proved
independently by M. Raum using a different approach. As an application, by
means of work of W. Zhang, modularity results for special cycles of codimension
2 on Shimura varieties associated to orthogonal groups can be derived.Comment: 8 pages, more details on Kudla's modularity conjecture included,
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Two applications of the curve lemma for orthogonal groups
We show (under some hypothesis in small dimensions) that the analytic degree
of the divisor of a modular form on the orthogonal group O(2,p) is determined
by its weight. Moreover, we prove that certain integrals, occurring in Arakelov
intersection theory, associated with modular forms on O(2,p) converge.Comment: 16 page
Sign changes of coefficients of half integral weight modular forms
For a half integral weight modular form we study the signs of the Fourier
coefficients . If is a Hecke eigenform of level with real
Nebentypus character, and is a fixed square-free positive integer with
, we show that for all but finitely many primes the sequence
has infinitely many signs changes. Moreover, we prove
similar (partly conditional) results for arbitrary cusp forms which are not
necessarily Hecke eigenforms
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