Results 1 to 10 of about 3,429,146 (271)
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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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, τ, subject to a particular inhomogeneous Laplace eigenvalue equation on the hyperbolic upper-half τ-plane.
Daniele Dorigoni, Rudolfs Treilis
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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 ℝ d−1 × 𝕋2 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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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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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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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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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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Analytic Continuation of Eisenstein Series [PDF]
Transactions of the American Mathematical Society, 1972 The classical Eisenstein series are essentially of the form Σ m , n ′ ( ( m + r 1 ) z + n +
Joseph Lewittes
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Eisenstein series and approximations to $\pi$ [PDF]
Illinois Journal of Mathematics, 2001 where |q| < 1. To the right of each equation in Q and R, Ramanujan entered an equality involving π and square roots. (For the integer 51, the linear equation and the equality involving π, in fact, are not recorded by Ramanujan.) The equations in Q and R cannot possibly hold for all values of q with |q| < 1.
Bruce C. Berndt, Heng Huat Chan
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Hankel determinants of Eisenstein series [PDF]
, 2000 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 $E_{14} ^4$.
Stephen C. Milne
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