Results 1 to 10 of about 3,473,158 (260)
Notes on massless scalar field partition functions, modular invariance and Eisenstein series [PDF]
Journal of High Energy Physics, 2021 The partition function of a massless scalar field on a Euclidean spacetime manifold ā dā1 Ć š2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed.
Francesco Alessio +2 more
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Two string theory flavours of generalised Eisenstein series [PDF]
Journal of High Energy Physics, 2023 Generalised Eisenstein series are non-holomorphic modular invariant functions of a complex variable, Ļ, subject to a particular inhomogeneous Laplace eigenvalue equation on the hyperbolic upper-half Ļ-plane.
Daniele Dorigoni, Rudolfs Treilis
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Combinatorial multiple Eisenstein series [PDF]
Research in the Mathematical Sciences, 2022 We construct a family of q -series with rational coefficients satisfying a variant of the extended double shuffle equations, which are a lift of a given $$\mathbb {Q}$$ Q -valued solution of the extended double shuffle equations.
Henrik Bachmann, Annika Burmester
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Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series [PDF]
Journal of High Energy Physics, 2018 We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Our formalism is based on a special case of a coaction on large classes of periods that is applied in particular to elliptic ...
Johannes Broedel +4 more
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On the local $L^2$ -Bound of the Eisenstein series [PDF]
Forum of Mathematics, Sigma, 2022 We study the growth of the local $L^2$ -norms of the unitary Eisenstein series for reductive groups over number fields, in terms of their parameters. We derive a poly-logarithmic bound on an average, for a large class of reductive groups.
Subhajit Jana, Amitay Kamber
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Eisenstein Series in String Theory [PDF]
Classical and Quantum Gravity, 1999 We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only.
Antoniadis I +31 more
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All modular forms of weight 2 can be expressed by Eisenstein series [PDF]
Research in Number Theory, 2020 We show that every elliptic modular form of integral weight greater than 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central L\documentclass[12pt]{
Martin Raum, Jiacheng Xia
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A construction of residues of Eisenstein series and relatedsquare-integrable classes in the cohomology of arithmetic groups of low k-rank [PDF]
Forum mathematicum, 2019 The cohomology of an arithmetic congruence subgroup of a connected reductive algebraic group defined over a number field is captured in the automorphic cohomology of that group.
Neven Grbac, Joachim Schwermer
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On constant terms of Eisenstein series [PDF]
Acta Arithmetica, 2020 We calculate the constant terms of certain Hilbert modular Eisenstein series at all cusps. Our formula relates these constant terms to special values of Hecke $L$-series.
S. Dasgupta, M. Kakde
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Higher d Eisenstein series and a duality-invariant distance measure [PDF]
Journal of High Energy PhysicsThe Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product E s (G, B) of the real analytic Eisenstein series $${E}_{
Nathan Benjamin, A. Liam Fitzpatrick
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