Results 21 to 30 of about 1,658 (186)

$1/8$-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

Congruences with Eisenstein series and -invariants [PDF]

Compositio Mathematica, 2019
We study the variation of $\unicode[STIX]{x1D707}$ -invariants in Hida families with residually reducible Galois representations.
Bellaïche, Joël, Pollack, Robert
openaire   +5 more sources

Eisenstein series in string theory [PDF]

Classical and Quantum Gravity, 2000
We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are manifestly invariant modular functions on the symmetric space K\G(R) of non-compact type, with K the maximal ...
Obers, Niels A., Pioline, Boris
openaire   +3 more sources

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
doaj   +1 more source

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
doaj   +1 more source

INTERLACING OF ZEROS OF EISENSTEIN SERIES

Kyushu Journal of Mathematics, 2021
Summary: Let \(E_k (z)\) be the normalized Eisenstein series of weight \(k\) for the full modular group \(\mathrm{SL} (2, \mathbb{Z})\). Let \(a > 0\) be an even integer. In this paper we completely determine when the zeros of \(E_k\) interlace with the zeros of \(E_{k+a}\). This generalizes a result of Nozaki on the interlacing of zeros of \(E_k\) and
GRIFFIN, Trevor, KENSHUR, Nathan, PRICE, Abigail, VANDENBERG-DAVES, Bradshaw, XUE, Hui, ZHU, Daozhou   +5 more
openaire   +2 more sources

ZEROS OF EISENSTEIN SERIES

Kyushu Journal of Mathematics, 2004
Let \(E_k\) be the normalized Eisenstein series of weight \(k\) with respect to the modular group \(\Gamma= \text{SL}_2(\mathbb{Z})\). It was shown by \textit{F. K. C. Rankin} and \textit{H. P. F. Swinnerton-Dyer} [Bull. Lond. Math. Soc. 2, 169--170 (1970; Zbl 0203.35504)] that all the zeros of \(E_k\) in the standard fundamental domain \({\mathcal F}\)
openaire   +3 more sources

MONTASE MEWUJUDKAN FANTASI DALAM FILM POHON PENGHUJAN

Capture, 2017
The research titled Montage Realizing Fantasy in the Rain Tree Film (Montase Mewujudkan Fantasi dalam Film Pohon Penghujan)uses qualitative research methods with a formalist esthetic approach and Eisenstein's montage theory.
Naafi Nur Rohma, Matius Ali
doaj   +1 more source