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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 ...
Siegfried Bocherer +1 more
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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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Automorphic L-functions of half-integral weight [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1978 I I Piatetski-Shapiro
exaly +2 more sources
Physics Letters B, 2015 A framework of inflation is formulated based on symmetry groups and their associated automorphic functions. In this setting the inflaton multiplet takes values in a curved target space constructed from a continuous group G and a discrete subgroup Γ.
Rolf Schimmrigk
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Black Hole Probes of Automorphic Space [PDF]
, 2012 Over the past few years the arithmetic Langlands program has proven useful in addressing physical problems. In this paper it is shown how Langlands' reciprocity conjecture for automorphic forms, in combination with a representation theoretic notion of ...
Schimmrigk, Rolf
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A General Framework of Automorphic Inflation [PDF]
, 2016 Automorphic inflation is an application of the framework of automorphic scalar field theory, based on the theory of automorphic forms and representations.
Schimmrigk, Rolf
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Automorphic Green functions on Hilbert modular surfaces
, 2023 36 pages; mostly results from the author's ...
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Modular Inflation Observables and $j$-Inflation Phenomenology [PDF]
, 2017 Modular inflation is the restriction to two fields of automorphic inflation, a general group based framework for multifield scalar field theories with curved target spaces, which can be parametrized by the comoving curvature perturbation ${\cal R}$ and ...
Schimmrigk, Rolf
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