Results 51 to 60 of about 3,473,158 (260)

A REMARK OF EISENSTEIN SERIES AND THETA SERIES [PDF]

Bulletin of the Korean Mathematical Society, 2002
The authors claim results of the kind \(\theta_3(\tau^2)^4= \theta_3(\tau)^4\), \(\Delta(\tau^2)= \Delta(\tau)\), \(J(\tau^2)= J(\tau)\) for some \(\tau\) in the upper half plane which belong to an imaginary quadratic number field. Here, \(\theta_3\) is the Jacobi theta function, \(\Delta\) is the modular discriminant, and \(J\) is the elliptic modular
Daeyeoul Kim, Ja Kyung Koo
openaire   +3 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

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

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

Eisenstein series and convolution sums [PDF]

The Ramanujan Journal, 2018
We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums $ \sum_{a+p b=n} (a) (b)$, $ \sum_{p_1a+p_2 b=n} (a) (b)$ and $ \sum_{a+p_1 p_2 b=n} (a) (b)$ where $p, p_1, p_2$ are primes.
openaire   +5 more sources

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

Effective counting for discrete lattice orbits in the plane via Eisenstein series [PDF]

L'Enseignement mathématique, 2019
We prove effective bounds on the rate in the quadratic growth asymptotics for the orbit of a non-uniform lattice of SL(2,R), acting linearly on the plane.
Claire Burrin, A. Nevo, Ren'e Ruhr, B. Weiss   +3 more
semanticscholar   +1 more source

Symmetries in A-type little string theories. Part II. Eisenstein series and generating functions of multiple divisor sums [PDF]

Journal of High Energy Physics, 2019
We continue our study of symmetries of a class of little string theories of A-type, which are engineered by N parallel M5-branes probing a flat transverse space.
Brice Bastian, S. Hohenegger
semanticscholar   +1 more source

Critical points of the classical Eisenstein series of weight two [PDF]

Journal of differential geometry, 2017
In this paper, we completely determine the critical points of the normalized Eisenstein series $E_2(\tau)$ of weight $2$. Although $E_2(\tau)$ is not a modular form, our result shows that $E_2(\tau)$ has at most one critical point in every fundamental ...
Zhijie Chen, Changshou Lin
semanticscholar   +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