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Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes

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 نشر من قبل Dohoon Choi
 تاريخ النشر 2007
  مجال البحث
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 تأليف Dohoon Choi




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Recently, Bruinier and Ono classified cusp forms $f(z) := sum_{n=0}^{infty} a_f(n)q ^n in S_{lambda+1/2}(Gamma_0(N),chi)cap mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen Bracket, we extend this result to modular forms of half integral weight for primes $p geq 5$. As applications of our main theorem we derive distribution properties, for modulo primes $pgeq5$, of traces of singular moduli and Hurwitz class number. We also study an analogue of Newmans conjecture for overpartitions.

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