Results 61 to 70 of about 3,429,146 (271)
Critical points of the classical Eisenstein series of weight two [PDF]
Journal of differential geometry, 2017 In this paper, we completely determine the critical points of the normalized Eisenstein series $E_2(\tau)$ of weight $2$. Although $E_2(\tau)$ is not a modular form, our result shows that $E_2(\tau)$ has at most one critical point in every fundamental ...
Zhijie Chen, Changshou Lin
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TomoCPT: a generalizable model for 3D particle detection and localization in cryo-electron tomograms. [PDF]
Acta Crystallogr D Struct BiolTomoCPT is a generalizable transformer‐based 3D particle‐picking tool for cryo‐tomographic data.Cryo‐electron tomography is a rapidly developing field for studying macromolecular complexes in their native environments and has the potential to revolutionize our understanding of protein function.
Shah PNM, Sanchez-Garcia R, Stuart DI.
europepmc +2 more sources
All modular forms of weight 2 can be expressed by Eisenstein series [PDF]
Research in Number Theory, 2019 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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Eisenstein series on loop groups [PDF]
Transactions of the American Mathematical Society, 2014 Based on Garland’s work, in this paper we construct the Eisenstein series on the adelic loop groups over a number field, induced from either a cusp form or a quasi-character which is assumed to be unramified. We compute the constant terms and prove their absolute and uniform convergence under the affine analog of Godement’s criterion.
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Utilization of Ramanujan-type Eisenstein series in the generation of differential equations
AIMS MathematicsIn his lost notebook, Ramanujan presented unique categories of remarkable infinite series, known as the Ramanujan-type Eisenstein series. The objective of this paper is to generate various differential identities related to classical $ \eta $-functions ...
H. C. Vidya, B. A. Rao
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Normalizations of Eisenstein integrals for reductive symmetric spaces
, 2017 We construct minimal Eisenstein integrals for a reductive symmetric space G/H as matrix coefficients of the minimal principal series of G. The Eisenstein integrals thus obtained include those from the \sigma-minimal principal series.
Ban, Erik P. van den, Kuit, Job J.
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Eisenstein Series and String Thresholds [PDF]
, 1998 We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $
Peixoto, M. M. +3 more
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Mock modular Eisenstein series with Nebentypus [PDF]
, 2019 By the theory of Eisenstein series, generating functions of various divisor functions arise as modular forms. It is natural to ask whether further divisor functions arise systematically in the theory of mock modular forms.
Michael H. Mertens, K. Ono, Larry Rolen
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Lacunary recurrences for Eisenstein series [PDF]
Research in Number Theory, 2015 6 pages, more detailed proofs in v3, accepted for publication in Research in Number ...
Michael H. Mertens, Larry Rolen
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New modular invariants in N $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory
Journal of High Energy Physics, 2021 We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the N $$ \mathcal{N} $$ = 4 SU(N) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ ...
Shai M. Chester +4 more
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