An Integral Representation of Standard Automorphic L Functions for Unitary Groups
International Journal of Mathematics and Mathematical Sciences, 2007 Let F be a number field, G a quasi-split unitary group of rank n. We show that given an irreducible cuspidal automorphic representation π of G(A), its (partial) L function LS(s,π,σ) can be represented by a Rankin-Selberg-type integral involving cusp ...
Yujun Qin
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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
Basis decompositions of genus-one string integrals
Journal of High Energy PhysicsOne-loop scattering amplitudes in string theories involve configuration-space integrals over genus-one surfaces with coefficients of Kronecker-Eisenstein series in the integrand.
Carlos Rodriguez +2 more
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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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Asymptotic expansions for a class of generalized holomorphic Eisenstein series, Ramanujan's formula for $ζ(2k+1)$, Weierstrass' elliptic and allied functions [PDF]
, 2022 Masanori Katsurada, Takumi Noda
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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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Faber's socle intersection numbers via Gromov–Witten theory of elliptic curve
Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2698-2707, September 2025.Abstract The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of Mg$\mathcal {M}_g$. This new proof exhibits a new beautiful tautological relation that stems from the recent work of Oberdieck–Pixton on the Gromov–Witten theory of the elliptic curve via a refinement of ...
Xavier Blot +2 more
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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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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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Note on Siegel-Eisenstein series [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1995 Let \(\Gamma_n(K)\) stand for the Siegel modular group if \(K=\mathbb{Q}\) resp. for the Hermitian modular group of degree \(n\) over \(K\) if \(K\) is an imaginary quadratic number field of class number 1. Denote by \(E^{(n)}_{k,K} (Z,s)\) the attached Siegel-Eisenstein series of weight \(k\) with factor of convergence \((\text{det Im} M \langle Z ...
openaire +2 more sources