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Automorphic Functions on Hecke Subgroups Associated with Generalized Modular Equation
BAUET Journal, 2023 Md Shafiul Alam
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Journal of Number Theory, 1999 Let \(f\) be a newform of weight \(k\) and trivial character with respect to \(\Gamma_0(N)\) for squarefree \(N\) and assume \(f\) has eigenvalue \(-1\) under the Fricke involution \(w_N\). In this paper, the authors characterize the vanishing of the central value \(L(f,k/2)\) of the \(L\)-function of \(f\) completely in terms of elementary properties ...
Böcherer, Siegfried +1 more
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Automorphic integrals with log-polynomial period functions and arithmetical identities [PDF]
Indagationes mathematicae, 2022 Building on the works of S. Bochner on equivalence of modular relation with functional equation associated to the Dirichlet series, K. Chandrasekharan and R.
Tewlede GEgziabher +2 more
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The sixth moment of automorphic L-functions [PDF]
Journal of Number Theory, 2021 We investigate the sixth moment of the family of $L$-functions associated to holomorphic modular forms on $GL_2$ with respect to a congruence subgroup $\Gamma_1(q)$. We improve on previous work and obtain an unconditional upper bound of the correct order
Joshua Stucky
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Mathematics, 2021 In this note, we propose a new construction of cyclotomic p-adic L-functions that are attached to classical modular cuspidal eigenforms. This allows for us to cover most known cases to date and provides a method which is amenable to generalizations to ...
Santiago Molina
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Two string theory flavours of generalised Eisenstein series
Journal of High Energy Physics, 2023 Generalised Eisenstein series are non-holomorphic modular invariant functions of a complex variable, τ, subject to a particular inhomogeneous Laplace eigenvalue equation on the hyperbolic upper-half τ-plane.
Daniele Dorigoni, Rudolfs Treilis
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Greens functions, Hamiltonians and modular automorphisms [PDF]
Communications in Mathematical Physics, 1976 We demonstrate, under circumstances that allow the construction of a “thermodynamic” hamiltonian, that Gibbs equilibrium states ω are modular states in the Tomita-Takesaki sense. The thermodynamic Greens functionsG are connected to these modular states, and the associated group of modular automorphisms σ, by the identification $$G(A, B; t) = \omega (
Bratteli, Ola, Robinson, Derek W.
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On Deligne's conjecture for symmetric fourth L-functions of Hilbert modular forms [PDF]
Advances in Mathematics, 2021 We prove Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms. We extend the result of Morimoto based on generalization and refinement of the results of Grobner and Lin to cohomological irreducible essentially conjugate self ...
Shih-Yu Chen
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Notices of the American Mathematical Society, 2021 The LMFDB is a database of mathematical objects and the connections between them. A web interface allows visitors to browse and query the database in a flexible and powerful way.
J. Cremona +3 more
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CM values of higher automorphic Green functions for orthogonal groups [PDF]
Inventiones Mathematicae, 2019 Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function Gs(z1,z2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}
J. Bruinier, Stephan Ehlen, Tonghai Yang
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