Results 61 to 70 of about 50,891 (201)
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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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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Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories [PDF]
, 2015 Kac-Moody groups $G$ over $\mathbb{R}$ have been conjectured to occur as symmetry groups of supergravities in dimensions less than 3, and their integer forms $G(\mathbb{Z})$ are conjecturally U-duality groups. Mathematical descriptions of $G(\mathbb{Z})$,
Bao, Ling, Carbone, Lisa
core
Geometric Eisenstein series: twisted setting
, 2016 Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X in the setting ...
Lysenko, Sergey
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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 meta-abelian elliptic KZB associator and periods of Eisenstein series
, 2017 We compute the image of Enriquez’ elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve.Our main result is an explicit formula for this image in terms of Eichler integrals of ...
Matthes, N.
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.Abstract String theory has strong implications for cosmology, implying the absence of a cosmological constant, ruling out single‐field slow‐roll inflation, and that black holes decay. The origins of these statements are elucidated within the string‐theoretical swampland programme.
Kay Lehnert
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Modular invariance in finite temperature Casimir effect
Journal of High Energy Physics, 2020 The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular ...
Francesco Alessio, Glenn Barnich
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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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