Results 31 to 40 of about 3,473,158 (260)
Eisenstein series of even weight $k \geq 2$ and integral binary quadratic forms [PDF]
Proceedings of the American Mathematical Society, 2020 We prove a conjecture of Matsusaka on the analytic continuationof hyperbolic Eisenstein series in weight $2$ on the full modular group $\mathrm{SL}_2(\mathbb{Z})$.
Andreas Mono
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A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS
Forum of Mathematics, Sigma, 2020 We introduce a new family of real-analytic modular forms on the upper-half plane. They are arguably the simplest class of ‘mixed’ versions of modular forms of level one and are constructed out of real and imaginary parts of iterated integrals of ...
FRANCIS BROWN
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Eisenstein Series and Approximations to π [PDF]
Illinois Journal of Mathematics, 2001 The first purpose of this paper is to elucidate some marginal notes of Ramanujan found in his ``lost notebook''. It turns out that these notes give relations between certain values of \(Q^3\) and \(R^2\) where \(Q\) and \(R\) are Ramanujan's usual notations for the Eisenstein series of weight 4 and 6.
Berndt, Bruce C., Chan, Heng Huat
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Schubert Eisenstein Series [PDF]
American Journal of Mathematics, 2014 We define Schubert Eisenstein series as sums like usual Eisenstein series but with the summation restricted to elements of a particular Schubert cell, indexed by an element of the Weyl group. They are generally not fully automorphic. We will develop some results and methods for ${\rm GL}_3$ that may be suggestive about the general case.
Bump, D, Choie, Y
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EISENSTEIN–KRONECKER SERIES VIA THE POINCARÉ BUNDLE
Forum of Mathematics, Sigma, 2019 A classical construction of Katz gives a purely algebraic construction of Eisenstein–Kronecker series using the Gauß–Manin connection on the universal elliptic curve. This approach gives a systematic way to study algebraic and $p$-adic properties of real-
JOHANNES SPRANG
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Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors [PDF]
, 2014 Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on Kac-Moody groups. In particular, we analyse the Eisenstein series on $E_9(R)$, $E_{10}(R)$ and $E_{11}(R)
Fleig, Philipp +2 more
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Little string instanton partition functions and scalar propagators
Journal of High Energy Physics, 2023 We discuss a class of Little String Theories (LSTs) whose low energy descriptions are supersymmetric gauge theories on the Ω-background with gauge group U(N) and matter in the adjoint representation. We show that the instanton partition function of these
Baptiste Filoche, Stefan Hohenegger
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Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series
Journal of Applied Mathematics, 2021 Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre’s arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using (p, k)-parametrization in terms of Borweins’
B. R. Srivatsa Kumar +2 more
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Effective Lower Bounds for L(1,{\chi}) via Eisenstein Series [PDF]
, 2016 We give effective lower bounds for $L(1,\chi)$ via Eisenstein series on $\Gamma_0(q) \backslash \mathbb{H}$. The proof uses the Maass-Selberg relation for truncated Eisenstein series and sieve theory in the form of the Brun-Titchmarsh inequality.
Humphries, Peter
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A fresh approach to classical Eisenstein series and the newer Hilbert–Eisenstein series [PDF]
International Journal of Number Theory, 2017 This paper is concerned with new results for the circular Eisenstein series [Formula: see text] as well as with a novel approach to Hilbert–Eisenstein series [Formula: see text], introduced by Michael Hauss in 1995. The latter turns out to be the product of the hyperbolic sinh function with an explicit closed form linear combination of digamma ...
Tibor K. Pogány +2 more
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