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Showing 1 to 18 of 18 for “"automorphic forms"”.
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p-adic L-functions of automorphic forms
… a number field, p a prime number. To an (adelic) automorphic representation of GL2 over F (with certain conditions at places above p and ∞) we construct a p-adic L-function which interpolates the complex (Jacquet-Langlands) L-function at the central critical point. This is a generalization of a …
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Boundary Value Problems Of Spaces Of Automorphic Forms
… natural self-adjoint operators on spaces of automorphic forms whose only possible discrete spectrum is λ s = s(s − 1) for s in a subset of on-line zeros of an L-function, appearing as a compact period of cuspidal-data Eisenstein series on GL 4 . These ideas have their origins in re- sults of …
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Topics on the Spectral Theory of Automorphic Forms
We study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's …
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p-arithmetic cohomology and p-adic automorphic forms
… representations can be described in terms of automorphic representations of the group. In this thesis, we prove similar results for the cohomology of an *S*-arithmetic groups (where *S* is a finite set of primes) with coefficients in different types of representations. For example, we show …
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Analytic and arithmetic applications of half integral weight automorphic forms
… applications of half integral weight modular forms. In the first chapter we are motivated by a conjecture of Hoffstein (2011) that asserts that the L-series attached to a half integral weight modular form satisfies a Lindelof hypothesis. Using spectral and diophantine techniques, the first …
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On the Construction of Certain Automorphic Forms of Non-Negative Dimension
Made available in DSpace on 2014-12-05T21:50:12Z (GMT). No. of bitstreams: 1 5900533.pdf: 1526892 bytes, checksum: 3cebc6d56e8de70ee4e4b8ad006ae56a (MD5) Previous issue date: 1958
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Higher Derivative Corrections to the Low-Energy E ective Action of Type IIA/B String Theory and M-theory
… coecient functions that transform as En+1 (Z) automorphic forms. These automorphic forms are complex mathematical objects that encode all the perturbative and non-perturbative features of type II string theory and M-theory compactied on an torus to d dimensions. We investigate the structure of …
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Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula
In their paper Metaplectic Forms, D. A. Kazhdan and S. J. Patterson developed a generalization of automorphic forms that are defined on metaplectic groups. These groups are non-trivial covering groups of usual algebraic groups, and the forms defined on them are representations that respect the …
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Whittaker functions on metaplectic groups
… of crucial importance in the classical study of automorphic forms on adele groups. Motivated by the appearance of Whittaker functions for covers of reductive groups in the theory of multiple Dirichlet series, we provide a study of Whittaker functions on metaplectic covers of reductive groups over …
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Singular theta lifts and near-central special values of Rankin-Selberg L-functions
… thesis we study integrals of a product of two automorphic forms of weight 2 on a Shimura curve over Q against a function on the curve with logarithmic singularities at CM points obtained as a Borcherds lift. We prove a formula relating periods of this type to a near-central special value of a …
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Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods
… Dirichlet series with functional equations and automorphic forms, there have been a great number of generalizations. Of particular interest is a generalization due to Bochner that gives a correspondence between Dirichlet series with any finite number of poles that satisfy the classical …
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p-adic L-functions and the Geometry of Hida Families
… theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor …
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Congruences in modular, Jacobi, Siegel, and mock modular forms with applications
… in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the primes for which there can be analogous congruences in the coefficients of the Fourier …
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Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions
A rising philosophy in the theory of automorphic representations in number theory is that higher central derivatives of L-functions of automorphic forms should correspond to the intersection numbers of special cycles on moduli spaces. A classic early result along this philosophy was achieved by …
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Nearby cycles and the cohomology of shtukas
… Lafforgue constructed Langlands parameters from automorphic forms for any reductive group over a function field using excursion operators. Our aim is to give a general approach for proving certain local-global compatibilities satisfied by these Langlands parameters. The main consequence for the …
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Sato-Tate Problem for GL(3)
… on the Kuznetsov trace formula of Maass forms for SL(3,Z), we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the p-th Hecke eigenvalue of Maass forms, with the rate of convergence. With a conjectured orthogonality relation …
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Behavior of partition values modulo powers of primes
… of a modular form. Using the theory of modular forms, we study the behavior of <italic>p(n)</italic> and related partition statistics and relate partition values to other objects of interest in the theory of automorphic forms, the central critical values of <italic>L</italic>-functions. </p> …
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ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|
Kronecker’s first limit formula describes the constant term in the Laurent expansion of a non-holomorphic Eisenstein series at one of its poles. Asai generalised the limit formula to Eisenstein series of level one defined for a number field with class number one and obtained a function analogous to …