Results 61 to 70 of about 52,441 (236)
Some Eisenstein Series Identities
Journal of Number Theory, 2000 In this paper, the author derives new proofs of Eisenstein series identities associated with the Borweins functions \(a(q)\), \(b(q)\) and \(c(q)\), defined by \[ \begin{aligned} a(q) &= \sum_{m,n=-\infty}^\infty q^{m^2+mn+n^2},\\ b(q) &= \sum_{m,n=-\infty}^\infty e^{2(m-n)\pi i/3}q^{m^2+mn+n^2},\\ \text{and} c(q) &=\sum_{m,n=-\infty}^\infty q^{(m+1/3)^
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Kac--Moody groups and automorphic forms in low dimensional supergravity theories
, 2016 Kac--Moody groups $G$ over $\mathbb{R}$ have been conjectured to occur as symmetry groups of supergravity theories dimensionally reduced to dimensions less than 3, and their integral forms $G(\mathbb{Z})$ conjecturally encode quantized symmetries.
Bao, Ling, Carbone, Lisa
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Generating series of all modular graph forms from iterated Eisenstein integrals
Journal of High Energy Physics, 2020 We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for their low ...
Jan E. Gerken +2 more
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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 \({\mathcal F}\)
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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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The Eisenstein elements of modular symbols for level product of two distinct odd primes
, 2015 We explicitly write down the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups {\Gamma}_0 (pq) with p and q distinct odd primes, giving an answer to a question of Merel in
Banerjee, Debargha +1 more
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Public Administration, Volume 103, Issue 4, Page 979-991, December 2025.ABSTRACT Representative bureaucracy theory posits that the presence of less‐advantaged social groups in public leadership positions is an important driver of social equity among the recipients of public services and the public servants who provide them.
Rhys Andrews
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Siegel Eisenstein series of degree n and Λ-adic Eisenstein series
Journal of Number Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Eisenstein series on loop groups [PDF]
Transactions of the American Mathematical Society, 2014 Based on Garland’s work, in this paper we construct the Eisenstein series on the adelic loop groups over a number field, induced from either a cusp form or a quasi-character which is assumed to be unramified. We compute the constant terms and prove their absolute and uniform convergence under the affine analog of Godement’s criterion.
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Character sum, reciprocity, and Voronoi formula
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3797-3823, December 2025.Abstract We prove a novel four‐variable character sum identity that serves as a twisted, non‐Archimedean analog of Weber's integrals for Bessel functions. Using this identity and ideas from Venkatesh's thesis, we provide a short spectral proof of the Voronoi formulae for classical modular forms with character twists.
Chung‐Hang Kwan, Wing Hong Leung
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