One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational
From MaRDI portal
Publication:4709943
DOI10.1070/RM2001v056n04ABEH000427zbMath1047.11072WikidataQ30052990 ScholiaQ30052990MaRDI QIDQ4709943
Publication date: 7 October 2003
Published in: Russian Mathematical Surveys (Search for Journal in Brave)
Related Items (41)
An Euler-type formula forβ(2n) and closed-form expressions for a class of zeta series ⋮ An elementary proof of Ramanujan's identity for odd zeta values ⋮ Generalization of the non-local derangement identity and applications to multiple zeta-type series ⋮ Irrationality of the sums of zeta values ⋮ On a continued fraction expansion for Euler's constant ⋮ Quantitative generalizations of Nesterenkos's linear independence criterion ⋮ Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function ⋮ A note on odd zeta values ⋮ Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials ⋮ Hahn multiple orthogonal polynomials of type I: hypergeometric expressions ⋮ A double inequality for the Apéry constant ⋮ Convolution of values of the Lerch zeta-function ⋮ A \(q\)-analogue of the Bailey-Borwein-Bradley identity ⋮ A new Ramanujan-type identity for \(L(2k+1, \chi_1)\) ⋮ GENERALIZED LAMBERT SERIES, RAABE’S COSINE TRANSFORM AND A GENERALIZATION OF RAMANUJAN’S FORMULA FOR ⋮ Relative cohomology of bi-arrangements ⋮ Padé approximants and balanced hypergeometric series. ⋮ Many odd zeta values are irrational ⋮ Construction of Approximations to Zeta-Values ⋮ A note on the number of irrational odd zeta values ⋮ Rapidly converging series for \(\zeta(2 n + 1)\) from Fourier series ⋮ Paperfolding infinite products and the gamma function ⋮ q-Analogues of Multiple Zeta Values and Their Application in Renormalization ⋮ Multiple series connected to Hoffman's conjecture on multiple zeta values ⋮ Diophantine approximation ⋮ Asymptotic results of the remainders in the series representations for the Apéry constant ⋮ Some evaluation of infinite series involving trigonometric and hyperbolic functions ⋮ On Ramanujan's formula for \(\zeta(1/2)\) and \(\zeta(2m+1)\) ⋮ The Hurwitz zeta function as a convergent series ⋮ Mellin transforms for multiple Jacobi-Piñeiro polynomials and a \(q\)-analogue ⋮ Well-poised hypergeometric series for Diophantine problems of zeta values ⋮ Unnamed Item ⋮ Irrationality of \(\zeta _{q}(1)\) and \(\zeta _{q}(2)\) ⋮ Structure of polyzetas and Lyndon words ⋮ On simultaneous Diophantine approximations to \(\zeta(2)\) and \(\zeta(3)\) ⋮ A note on values of the Dedekind zeta-function at odd positive integers ⋮ Koshliakov zeta functions I: modular relations ⋮ Generalized Lambert series and arithmetic nature of odd zeta values ⋮ Life and Mathematics of Alfred Jacobus van der Poorten (1942–2010) ⋮ Euler’s constant: Euler’s work and modern developments ⋮ On the transcendence of critical Hecke \(L\)-values
This page was built for publication: One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational