Automorphic L-functions of half-integral weight
نویسندگان
چکیده
منابع مشابه
Integral Moments of Automorphic L–functions
We obtain second integral moments of automorphic L–functions on adele groups GL2 over arbitrary number fields, by a spectral decomposition using the structure and representation theory of adele groups GL1 and GL2. This requires complete reformulation of the notion of Poincaré series, replacing the collection of classical Poincaré series over GL2(Q) or GL2(Q(i)) with a single, coherent, global o...
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We consider the higher integral moments for automorphic L-functions in short intervals and give a proof for the conjecture of Conrey et al. under Generalized Riemann Hypothesis for automorphic L-function.
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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 کاملOn Hecke L-functions attached to half-integral weight modular forms
We would like to recall that in the case of Hecke eigenforms on Γ1 non-vanishing results for their Hecke L-functions at an arbitrary point s0 in the critical strip (not on the critical line) have been proved in [4] (cf. also [7]), using holomorphic kernel functions. This method was carried over to the case of half-integral weight in [8], for arbitrary level. However, in this approach for given ...
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PREFACE This article follows the format of five lectures that we gave on automorphic Lfunctions. The lectures were intended to be a brief introduction for number theorists to some of the main ideas in the subject. Three of the lectures concerned the general properties of automorphic L-functions, with particular reference to questions of spectral decomposition. We have grouped these together as ...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1978
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.75.4.1620