Results 131 to 140 of about 3,473,158 (260)

Hankel Determinants of Eisenstein Series [PDF]

, 2001
In this paper we prove Garvan's conjectured formula for the square of the modular discriminant $ $ as a 3 by 3 Hankel determinant of classical Eisenstein series $E_{2n}$. We then obtain similar formulas involving minors of Hankel determinants for $E_{2r} ^m$, for $m=1,2,3$ and $r=2,3,4,5,7$, and $E_{14} ^4$.
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On Eisenstein series of degree two [PDF]

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1987
The paper contains results on analytic continuation of Eisenstein series and on functional equations, which have the following interesting corollary: Let \(f(Z)=\sum a(N) \exp (2\pi i \text{tr}(NZ)/q)\) be a cusp form of level \(q\), weight \(k\) of degree 2.
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Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
doaj   +1 more source

Eisenstein series and the top degree cohomology of arithmetic subgroups of SL _n /ℚ [PDF]

, 2021
Joachim Schwermer
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Cancellation of divergences up to three loops in exceptional field theory

Journal of High Energy Physics, 2018
We consider the tetrahedral three-loop diagram in E d exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes to the ∇6 R 4 term in the low-energy effective action for M ...
Guillaume Bossard, Axel Kleinschmidt
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Computations of Eisenstein series on Fuchsian groups [PDF]

, 2008
Helen Avelin
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Orthogonal Eisenstein series at harmonic points and modular forms of singular weight [PDF]

, 2022
Paul Kiefer
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Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Forum of Mathematics, Sigma
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over
Jan H. Bruinier, Yingkun Li, Tonghai Yang   +2 more
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Maass operators and Eisenstein series

Mathematische Annalen, 1981
Let ~ = G/K be a Hermitian symmetric space of the non-compact type, and let F C G be an arithmetic subgroup. It is obvious that the enveloping algebra U(g 0 of the complexified Lie algebra of G gives rise to operators which transform automorphic forms on N with respect to F to F-automorphic forms of a different type.
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Towards the n-point one-loop superstring amplitude. Part III. One-loop correlators and their double-copy structure

Journal of High Energy Physics, 2019
In this final part of a series of three papers, we will assemble supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued.
Carlos R. Mafra, Oliver Schlotterer
doaj   +1 more source