Integral moments of L-functions
نویسندگان
چکیده
منابع مشابه
Integral Moments of L-functions
We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary, orthogonal, or symplectic matrices, where the mom...
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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...
متن کاملun 2 00 2 INTEGRAL MOMENTS OF L - FUNCTIONS
Abstract. We give a new heuristic for all of the main terms in the integral moments of various families of L-functions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary, orthogonal, or symplectic matrices, where the mom...
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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.
متن کاملNatural Boundaries and a Correct Notion of Integral Moments of L–functions
It is shown that a large class of multiple Dirichlet series which arise naturally in the study of moments of L–functions have natural boundaries. As a remedy we consider a new class of multiple Dirichlet series whose elements have nice properties: a functional equation and meromorphic continuation. This class suggests the correct notion of integral moments of L–functions. §
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2005
ISSN: 0024-6115,1460-244X
DOI: 10.1112/s0024611504015175