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Automorphic L -functions of half-integral weight [PDF]
Proceedings of the National Academy of Sciences, 1978 We describe a theory of Whittaker models and L -functions for irreducible representations of a metaplectic covering group of GL (2). We explain how to use these L -functions to establish an arithmetical correspondence between “genuine” cuspidal representations of the ...
Gelbart, Stephen S. +1 more
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Lifting congruences to half-integral weight [PDF]
Research in Number Theory, 2022 Let \(\kappa \geq 6\) be an even integer and suppose that \(f\) and \(g\) be normalized newforms of weight \(\kappa\) for a subgroup of modular forms of odd and square-free level. Then in the paper under review, with the help of Saito-Kurokawa lifts and under weak conditions, the authors show that there exists an interesting congruence of Fourier ...
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Journal of Function Spaces, 2020 Let Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple ...
Qiang Chen, Bing He, Yong Hong, Zhen Li
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Mathematics, 2020 In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further ...
Jianquan Liao, Shanhe Wu, Bicheng Yang
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Integrating three-loop modular graph functions and transcendentality of string amplitudes
Journal of High Energy Physics, 2022 Modular graph functions (MGFs) are SL(2, ℤ)-invariant functions on the Poincaré upper half-plane associated with Feynman graphs of a conformal scalar field on a torus.
Eric D’Hoker, Nicholas Geiser
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Endpoint contributions to excited-state modular Hamiltonians
Journal of High Energy Physics, 2020 We compute modular Hamiltonians for excited states obtained by perturbing the vacuum with a unitary operator. We use operator methods and work to first order in the strength of the perturbation.
Daniel Kabat +3 more
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Frontiers in Digital Health, 2021 Parents/caregivers are consistently described as integral targets given their influential role in supporting and managing behaviors such as diet and physical activity.
Jennifer Sanchez-Flack +8 more
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Subconvexity for half integral weight L-functions [PDF]
Mathematische Zeitschrift, 2015 33 ...
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The half-integral weight eigencurve [PDF]
Algebra & Number Theory, 2008 In this paper we define Banach spaces of overconvergent half-integral weight $p$-adic modular forms and Banach modules of families of overconvergent half-integral weight $p$-adic modular forms over admissible open subsets of weight space. Both spaces are equipped with a continuous Hecke action for which $U_{p^2}$ is moreover compact.
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Period functions of half-integral weight modular forms [PDF]
Journal de théorie des nombres de Bordeaux, 2015 In this paper, we study the Eichler cohomology associated with half-integral weight cusp forms using the Dedekind eta function η(z) and the theta function θ(z). We prove that η-multiplication (resp. θ-multiplication) gives an isomorphism between the space of cusp forms of a half-integral weight and the cohomology group associated with the space η𝒫 ...
Choi, Dohoon, Lim, Subong, Raji, Wissam
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