Results 21 to 30 of about 3,429,146 (271)
Fourier expansion of light‐cone Eisenstein series [PDF]
Journal of the London Mathematical Society, 2022 In this work, we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1$n+1$ ‐space.
Dubi Kelmer, Shucheng Yu
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Orthogonal Eisenstein Series and Theta Lifts [PDF]
International Journal of Number Theory, 2021 We show that the additive Borcherds lift of vector-valued non-holomorphic Eisenstein series are orthogonal non-holomorphic Eisenstein series for $O(2, l)$.
P. Kiefer
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Semi-modular forms from Fibonacci–Eisenstein series [PDF]
The Ramanujan journal, 2021 In a 2021 paper, M. Just and the second author defined a class of “semi-modular forms” on $${\mathbb {C}}\backslash {\mathbb {R}}$$ C \ R , in analogy with classical modular forms, that are “half modular” in a particular sense; and constructed families ...
A. Akande, Robert Schneider
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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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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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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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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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Schubert Eisenstein Series [PDF]
American Journal of Mathematics, 2014 We define Schubert Eisenstein series as sums like usual Eisenstein series but with the summation restricted to elements of a particular Schubert cell, indexed by an element of the Weyl group. They are generally not fully automorphic. We will develop some results and methods for ${\rm GL}_3$ that may be suggestive about the general case.
Bump, D, Choie, Y
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