Results 11 to 20 of about 118 (89)

Algorithms and tools for iterated Eisenstein integrals

Journal of High Energy Physics, 2020
We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the parameter space ...
Claude Duhr, Lorenzo Tancredi
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Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series

Journal of High Energy Physics, 2018
We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Our formalism is based on a special case of a coaction on large classes of periods that is applied in particular to elliptic ...
Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi   +4 more
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Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series

Journal of Applied Mathematics, 2021
Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre’s arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using (p, k)-parametrization in terms of Borweins’
B. R. Srivatsa Kumar, Shruthi, D. Anu Radha   +2 more
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One-loop open-string integrals from differential equations: all-order α′-expansions at n points

Journal of High Energy Physics, 2020
We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless n-point one-loop amplitudes of open superstrings and open bosonic strings.
Carlos R. Mafra, Oliver Schlotterer
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$1/8$-BPS couplings and exceptional automorphic functions

SciPost Physics, 2020
Unlike the $R^4$ and $\nabla^4 R^4$ couplings, whose coefficients are Langlands--Eisenstein series of the U-duality group, the coefficient $\mathcal{E}^{(d)}_{(0,1)}$ of the $\nabla^6 R^4$ interaction in the low-energy effective action of type II strings
Guillaume Bossard, Axel Kleinschmidt, Boris Pioline
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On average theta functions of certain quadratic forms as sums of Eisenstein series

Open Mathematics, 2023
Let QQ be an integral positive definite quadratic form of level NN in 2k2k variables. Further, we assume that (−1)kN{\left(-1)}^{k}N is a fundamental discriminant. We express the average theta function of QQ as an explicit sum of Eisenstein series, which
Eum Ick Sun
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Linear dependence of quasi-periods over the rationals

Comptes Rendus. Mathématique, 2021
In this note we shall show that a lattice $\mathbb{Z}\omega _1+\mathbb{Z}\omega _2$ in $\mathbb{C}$ has $\mathbb{Q}$-linearly dependent quasi-periods if and only if $\omega _2/\omega _1$ is equivalent to a zero of the Eisenstein series $E_2$ under the ...
Kumar, K. Senthil
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Whittaker coefficients of geometric Eisenstein series

Forum of Mathematics, Sigma
Geometric Langlands predicts an isomorphism between Whittaker coefficients of Eisenstein series and functions on the moduli space of $\check {N}$ -local systems.
Jeremy Taylor
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Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions

Journal of Applied Mathematics, 2012
Based on the theories of Ramanujan's elliptic functions and the (p, k)-parametrization of theta functions due to Alaca et al. (2006, 2007, 2006) we derive certain Eisenstein series identities involving the Borweins' cubic theta functions with the help of
Ernest X. W. Xia, Olivia X. M. Yao
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Virasoro blocks at large exchange dimension

Nuclear Physics B, 2021
In this paper, we analyze Virasoro conformal blocks in the limit when the operator exchange dimension is taking to be large in comparison with the other parameters dependence of the block. We do this by using Zamolodchikov's recursion relations. We found
Carlos Cardona
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