On the Fourier Coefficients of Modular Forms of Half-integral Weight
نویسنده
چکیده
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, PB×).
منابع مشابه
Congruences for Fourier Coefficients of Half-integral Weight Modular Forms and Special Values of L−functions
Congruences for Fourier coefficients of integer weight modular forms have been the focal point of a number of investigations. In this note we shall exhibit congruences for Fourier coefficients of a slightly different type. Let f(z) = P∞ n=0 a(n)q n be a holomorphic half integer weight modular form with integer coefficients. If ` is prime, then we shall be interested in congruences of the form
متن کاملChanges of Fourier Coefficients 6 of Half - Integral Weight Cusp Forms
Let k be a positive integer. Suppose that f is a modular form of weight k + 1/2 on Γ0(4). The Shimura correspondence defined in [12] maps f to a modular form F of integral weight 2k. In addition, if f is an eigenform of the Hecke operator Tk+1/2(p), then F is also an eigenform of the Hecke operators T2k(p) with the same eigenvalue. For more on half-integral weight modular forms, see [12]. Let t...
متن کاملFe b 20 16 SIGN CHANGES OF FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF INTEGRAL WEIGHT , 2
In this paper, we investigate the sign changes of Fourier coefficients of half-integral weight Hecke eigenforms and give two quantitative results on the number of sign changes.
متن کاملSign Changes of Coefficients of Half Integral Weight Modular Forms
For a half integral weight modular form f we study the signs of the Fourier coefficients a(n). If f is a Hecke eigenform of level N with real Nebentypus character, and t is a fixed square-free positive integer with a(t) 6= 0, we show that for all but finitely many primes p the sequence (a(tp2m))m has infinitely many signs changes. Moreover, we prove similar (partly conditional) results for arbi...
متن کاملRandom 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...
متن کامل