Results 51 to 60 of about 3,429,146 (271)
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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Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms
Transactions of the London Mathematical Society, 2020 We define twisted Eisenstein series Es±(h,k;τ) for s∈C , and show how their associated period functions, initially defined on the upper half complex plane H , have analytic continuation to all of C′:=C∖R⩽0 . We also use this result, as well as properties
A. Folsom
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Dedekind sums arising from newform Eisenstein series [PDF]
International Journal of Number Theory, 2019 For primitive nontrivial Dirichlet characters [Formula: see text] and [Formula: see text], we study the weight zero newform Eisenstein series [Formula: see text] at [Formula: see text]. The holomorphic part of this function has a transformation rule that
Tristie Stucker, A. Vennos, M. Young
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On multiple series of Eisenstein type [PDF]
The Ramanujan Journal, 2015 The aim of this paper is to study certain multiple series which can be regarded as multiple analogues of Eisenstein series. As a prior research, the second-named author considered double analogues of Eisenstein series and expressed them as polynomials in terms of ordinary Eisenstein series.
Henrik Bachmann, Hirofumi Tsumura
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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 +3 more
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On the meromorphic continuation of Eisenstein series
Journal of the American Mathematical Society, 2023 Eisenstein series are ubiquitous in the theory of automorphic forms. The traditional proofs of the meromorphic continuation of Eisenstein series, due to Selberg and Langlands, start with cuspidal Eisenstein series as a special case, and deduce the general case from spectral theory.
Bernstein, J., Lapid, E.
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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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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
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MODULI INTERPRETATION OF EISENSTEIN SERIES [PDF]
International Journal of Number Theory, 2012 Let ℓ ≥ 3. Using the moduli interpretation, we define certain elliptic modular forms of level Γ(ℓ) over any field k where 6ℓ is invertible and k contains the ℓth roots of unity. These forms generate a graded algebra [Formula: see text], which, over C, is generated by the Eisenstein series of weight 1 on Γ(ℓ).
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