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Ramanujan’s Formula for ζ(2n + 1) (Q5038222)

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scientific article; zbMATH DE number 7594891

Language	Label	Description	Also known as
English	Ramanujan’s Formula for ζ(2n + 1)	scientific article; zbMATH DE number 7594891

Statements

scholarly article

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Ramanujan’s Formula for ζ(2n + 1) (English)

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Bruce C. Berndt

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Exploring the Riemann Zeta Function

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publication date

30 September 2022

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full work available at URL

https://arxiv.org/abs/1701.02964

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zbMATH Keywords

Euler's formula

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MaRDI profile type

MaRDI publication profile

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Ramanujan's Lost Notebook

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Generalized Dedekind sums and transformation formulae of certain Lambert series

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Generalized Dedekind Eta-Functions and Generalized Dedekind Sums

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Dedekind Sums and a Paper of G. H. Hardy

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Modular transformations and generalizations of several formulae of Ramanujan

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Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.

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On a secant Dirichlet series and Eichler integrals of Eisenstein series

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Über die Transformationsformel von \(\log \eta (\tau)\) und gewisser Lambertscher Reihen

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Invarianten linearer Differentialgleichungen

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Series acceleration formulas for Dirichlet series with periodic coefficients

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Hecke's functional equation and arithmetical identities

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The Nontrivial Zeros of Period Polynomials of Modular Forms Lie on the Unit Circle

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Unimodularity of zeros of period polynomials of Hecke eigenforms

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Eine einheitliche Herleitung einer gewissen Klasse von Transformationsformeln der analytischen Zahlentheorie (I)

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Remarks concerning the values of the Riemann zeta function at integral, odd arguments

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Comments on some formulae of Ramanujan

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FUNCTIONAL EQUATIONS AND SELF-RECIPROCAL FUNCTIONS CONNECTED WITH LAMBERT SERIES

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SOME RAPIDLY CONVERGENT SERIES FOR THE RIEMANN ξ-FUNCTION

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Transcendental values of certain Eichler integrals

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The transformation formula for the Dedekind modular function and related functional equations

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Riemann hypothesis for period polynomials of modular forms

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On rapidly convergent series for the Riemann zeta-values via the modular relation

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On Ramanujan's formula for values of Riemann zeta-function at positive odd integers

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Zeta-functions, Lambert series and arithmetic functions analogous to Ramanujan's ...-function. II.

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Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function

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Complete asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae–Jackson type

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Barnes multiple zeta-functions, Ramanujan's formula, and relevant series involving hyperbolic functions

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A generalization of Siegel's method

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Variations of the Ramanujan polynomials and remarks on \(\zeta(2j+1)/\pi^{2j+1}\)

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Unimodularity of zeros of self-inversive polynomials

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Period functions for Maass wave forms. I.

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Generalized Eisenstein series and several modular transformation formulae

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Infinite series identities from modular transformation formulas that stem from generalized Eisenstein series

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CHARACTER ANALOGUES OF INFINITE SERIES FROM A CERTAIN MODULAR TRANSFORMATION FORMULA

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Über gewisse Lambertsche Reihen. I: Verallgemeinerung der Modulfunktion \(\eta(\tau)\) und ihrer Dedekindschen Transformationsformel

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Modular forms and period polynomials

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Some series related to infinite series given by Ramanujan

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Some Infinite Series

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A simple proof of η(— 1/τ)= η(τ)√τ/i

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On the values of the Epstein zeta function

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On Plouffe's Ramanujan identities

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Periods of modular forms and Jacobi theta functions

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Identifiers

zbMATH Open document ID

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10.1007/978-3-319-59969-4_2

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5038222

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