Results 21 to 30 of about 52,441 (236)

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
doaj   +1 more source

On cubic multisections of Eisenstein series [PDF]

, 2013
A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three.
Alaniz, Andrew, Huber, Tim
core   +3 more sources

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
doaj   +1 more source

Eisenstein series for infinite-dimensional U-duality groups [PDF]

, 2012
We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes.
A Basu, A Basu, A Font, A Kleinschmidt, A Kleinschmidt, A Kleinschmidt, A Kleinschmidt, A Sen, Axel Kleinschmidt, B Julia, B Julia, B Pioline, B Pioline, B Pioline, C Hull, C Moeglin, D Ginzburg, D Kazhdan, D Maison, DH Peterson, DJ Gross, E Cremmer, E Cremmer, E Cremmer, E Kiritsis, F Englert, F Gubay, G Bossard, G Bossard, G Bossard, H Garland, H Garland, H Nicolai, H Nicolai, I Antoniadis, J Brown, K Meissner, K Narain, L Bao, L Bao, M Blau, MB Green, MB Green, MB Green, MB Green, MB Green, MB Green, MB Green, MB Green, MB Green, MB Green, N Beisert, N Lambert, N Lambert, N Obers, N Obers, N Obers, P Breitenlohner, PC West, Philipp Fleig, R Kallosh, RP Geroch, RP Langlands, S Elitzur, S Kudla, S Mizoguchi, T Damour, T Damour, T Damour, T Damour, T Damour, V Belinskii, V Kac, VG Kac, Y Michel   +74 more
core   +2 more sources

On Drinfeld modular forms of higher rank II [PDF]

, 2017
We show that the absolute value $|f|$ of an invertible holomorphic function $f$ on the Drinfeld symmetric space $\OM^r$ $(r \geq 2)$ is constant on fibers of the building map to the Bruhat-Tits building $\MB\MT$.
Gekeler, Ernst-Ulrich
core   +4 more sources

$1/8$-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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Utilization of Ramanujan-type Eisenstein series in the generation of differential equations

AIMS Mathematics
In his lost notebook, Ramanujan presented unique categories of remarkable infinite series, known as the Ramanujan-type Eisenstein series. The objective of this paper is to generate various differential identities related to classical $ \eta $-functions ...
H. C. Vidya, B. A. Rao
doaj   +1 more source

Normalizations of Eisenstein integrals for reductive symmetric spaces

, 2017
We construct minimal Eisenstein integrals for a reductive symmetric space G/H as matrix coefficients of the minimal principal series of G. The Eisenstein integrals thus obtained include those from the \sigma-minimal principal series.
Ban, Erik P. van den, Kuit, Job J.
core   +1 more source