Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms
نویسندگان
چکیده
منابع مشابه
Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms
Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of conjectures concerning the value-distribution of the Fourier coefficients of half-integral weight modular forms related to these L-functions. Our conjectures ma...
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S. Chowla conjectured that every prime p has the property that there are infinitely many imaginary quadratic fields whose class number is not a multiple of p. Gauss’ genus theory guarantees the existence of infinitely many such fields when p = 2, and the work of Davenport and Heilbronn [D-H] suffices for the prime p = 3. In addition, the DavenportHeilbronn result demonstrates that a positive pr...
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Let f(z) = ∑ n≥1 ane 2πinz be a Hecke eigenform of half-integral weightm+1/2, and let g(z) = ∑ n≥1 bne 2πinz be the corresponding even-weight form, in the sense of [Sh 73]. In particular, g has weight 2m, and belongs to the same eigenvalues of Hecke operators as f . If n = qr with squarefree r, then an is expressible in terms of ar and the {bj}. At the end of [Sh 77], Shimura suggested that ar ...
متن کاملOn the Fourier Coefficients of Modular Forms of Half-integral Weight
We obtain a formula relating the Fourier coefficients of a modular form of half-integral weight (that is constructed as a theta lift from an indefinite quaternion algebra B over Q) to the special values of L-functions. This formula has applications to proving the nonvanishing of a certain explicit theta lift and to an explicit version of the Rallis inner product formula for the dual pair (S̃L2, ...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2006
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2006.10128953