Results 21 to 30 of about 3,473,158 (260)
Poincaré series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms
Journal of High Energy Physics, 2022 We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincaré series in a companion paper. The source term of the Laplace equation is a product of (derivatives of)
Daniele Dorigoni +2 more
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A STIELTJES SEPARATION PROPERTY OF ZEROS OF EISENSTEIN SERIES
Kyushu Journal of Mathematics, 2022 . For k < (cid:96) , let E k ( z ) and E (cid:96) ( z ) be Eisenstein series of weights k and (cid:96) , respectively, for SL 2 ( Z ) . We prove that between any two zeros of E k ( e i θ ) there is a zero of E (cid:96) ( e i θ ) on the interval π/ 2 < θ <
William Frendreiss +5 more
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Geometric Eisenstein series [PDF]
Inventiones mathematicae, 2002 The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence. Our construction is based on the study of certain relative compactification of the moduli stack of parabolic bundles on a curve suggested by V.Drinfeld.
Alexander Braverman, Dennis Gaitsgory
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Cusps, Kleinian groups, and Eisenstein series
Forum of Mathematics, Sigma, 2023 We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group $\Gamma
Beibei Liu, Shi Wang
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Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems
Journal of High Energy Physics, 2022 We derive new Poincaré-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one.
Daniele Dorigoni +2 more
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INTERLACING OF ZEROS OF EISENSTEIN SERIES
Kyushu Journal of Mathematics, 2021 . Let E k ( z ) be the normalized Eisenstein series of weight k for the full modular group SL ( 2 , Z ) . Let a > 0 be an even integer. In this paper we completely determine when the zeros of E k interlace with the zeros of E k + a .
Trevor Griffin +5 more
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Quantum ergodicity for Eisenstein series on hyperbolic surfaces of large genus [PDF]
Mathematische Annalen, 2020 We give a quantitative estimate for the quantum mean absolute deviation on hyperbolic surfaces of finite area in terms of geometric parameters such as the genus, number of cusps and injectivity radius.
Etienne Le Masson, Tuomas Sahlsten
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Critical points of Eisenstein series [PDF]
Mathematika, 2020 For any even integer k⩾4$k {\nobreakspace \geqslant \nobreakspace }4$ , let Ek be the normalized Eisenstein series of weight k for SL2(Z)${\bf SL}_2({\bf Z})$ . Also let D be the closure of the standard fundamental domain of the Poincaré upper half plane
S. Gun, Joseph Oesterl'e
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Elliptic modular graph forms. Part I. Identities and generating series
Journal of High Energy Physics, 2021 Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker-Eisenstein series. The simplest
Eric D’Hoker +2 more
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Lotman about Eisenstein: Context Reconstruction [PDF]
Литературный факт, 2023 Ethics played an important role for Yu.M. Lotman when he judged some phenomenon of art or the personality of the creator. He thought filmmaker S.M. Eisenstein was a brilliant avant-garde artist, though indifferent to moral issues, and therefore condemned
Tatyana D. Kuzovkina
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