2011/10/28 by Lynne H. Walling, Walling, Lynne H.
Mathematics · #11F27 #11F30 Secondary #11F37 #11F46 Primary #11F60 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1110.6351
openalex publication_date 2011/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce an alternate set of generators for the Hecka algebra, and give\nan explicit formula for the action of these operators on Fourier coefficients.\nWith this, we compute the eigenvalues of Hecke operators acting on average\nSiegel theta series with half-integral weight (provided the prime associated to\nthe operators does not divide the level of the theta series). Next, we bound\nthe eigenvalues of these operators in terms of bounds on Fourier coefficients.\nThen we show that the half-integral weight Kitaoka subspace is stable under all\nHecke operators. Finally, we observe that an obvious isomorphism between Siegel\nmodular forms of weight k+1/2 and "even" Jacobi modular forms of weight k+1\nis Hecke-invariant (here the level and character are arbitrary).\n