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This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured… (More)

We establish the meromorphic continuation of a multiple Dirichlet series associated to the fourth moment of quadratic Dirichlet L-functions, over the rational function field Fq(T ) with q odd, up to its natural boundary. This is the first such result in which the group of functional equations is infinite; in such cases, it is expected that the series cannot… (More)

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… (More)

- A. Diaconu, P. Garrett, P. GARRETT
- 2009

We break the convexity bound in the t–aspect for L–functions attached to cuspforms f for GL2(k) over arbitrary number fields k. The argument uses asymptotics with error term with a power saving, for second integral moments over spectral families of twists L(s, f ⊗χ) by grossencharacters χ, from our previous paper [Di-Ga]. §0. Introduction In many instances,… (More)

- Adrian Diaconu, Florin Manea, Catalin Tiseanu
- FCT
- 2009

We exhibit a spectral identity involving L(s,Symf) for f on SL2. Perhaps contrary to expectations, we do not treat L(s,Symf) directly as a GL3 object. Rather, we take advantage of the coincidence that the standard L-function for SL2 is the symmetric square for a cuspform on GL2 restricted to SL2. [1] As SL2 = Sp2, the integral identities obtained from Sp2n… (More)

- A. Diaconu, P. Garrett
- 2009

1. The moment expansion 2. Spectral expansion: reduction to GL2 3. Spectral expansion for GL2 4. Continuation and holomorphy at s′ = 0 for GL2 5. Spectral expansion for GLr 6. Continuation and holomorphy at s′ = 0 for GLr 7. Appendix: half-degenerate Eisenstein series 8. Appendix: Eisenstein series for GL2 9. Appendix: residues of degenerate Eisenstein… (More)

- T. Sivakumar, R. Venkatesan, +17 authors Fawad Ahmed
- 2014

Information security has become an important issue for data storage and transmission due to growth of communication development and exchange of sensitive information through Internet. The services like confidentiality, integrity, and digital signature are required to protect data against unauthorized modification and misuse by anti social elements. Image… (More)

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… (More)

- ADRIAN DIACONU, YE TIAN
- 2008