ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL MODULAR FORMS
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Abstract We prove that if F is a nonzero (possibly noncuspidal) vector-valued Siegel modular form of any degree, then it has infinitely many nonzero Fourier coefficients which are indexed by half-integral matrices having odd, square-free (and thus fundamental) discriminant. The proof uses an induction argument in the setting of vector-valued modular forms. Further, as an application of a variant of our result and complementing the work of A. Pollack, we show how to obtain an unconditional proof of the functional equation of the spinor L-function of a holomorphic cuspidal Siegel eigenform of degree $3$ and level $1$ .
2002 ◽
Vol 65
(2)
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pp. 239-252
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1997 ◽
Vol 147
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pp. 71-106
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2019 ◽
Vol 15
(05)
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pp. 907-924
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2014 ◽
Vol 57
(3)
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pp. 485-494
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