Relations for Bernoulli–Barnes numbers and Barnes zeta functions

DOI10.1142/S1793042114500298zbMath1369.11018arXiv1301.7097OpenAlexW1973593442WikidataQ114072042 ScholiaQ114072042MaRDI QIDQ2876607

Matthias Beck, Abdelmejid Bayad

Publication date: 19 August 2014

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7097

zbMATH Keywords

reciprocity lawBarnes zeta functionFourier-Dedekind sumBernoulli-Barnes polynomialBernoulli-Barnes number

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Dedekind eta function, Dedekind sums (11F20) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (15)

On the restricted partition function ⋮ On the asymptotic distribution of cranks and ranks of cubic partitions ⋮ Zeta functions interpolating the convolution of the Bernoulli polynomials ⋮ On the restricted partition function via determinants with Bernoulli polynomials ⋮ Correction to the leading term of asymptotics in the problem of counting the number of points moving on a metric tree ⋮ Explicit computations of some spectral invariants of compact symmetric spaces of rank one ⋮ A higher-order convolution for Bernoulli polynomials of the second kind ⋮ Formulae bringing to light from certain classes of numbers and polynomials ⋮ New characterization of Appell polynomials ⋮ Multivariable Faulhaber-type formulas and Barnes zeta functions ⋮ An explicit form of the polynomial part of a restricted partition function ⋮ A symbolic approach to some identities for Bernoulli–Barnes polynomials ⋮ A study of Möbius-Bernoulli numbers ⋮ On the restricted partition function via determinants with Bernoulli polynomials. II ⋮ Representations for the derivative at zero and finite parts of the Barnes zeta function

Cites Work

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• Barnes' double zeta function, the Dedekind sum and Ramanujan's formula
• Barnes' multiple zeta function and Apostol's generalized Dedekind sum
• Sums of products of Bernoulli numbers
• Generalized Dedekind sums and transformation formulae of certain Lambert series
• Identities concerning Bernoulli and Euler polynomials
• Computing the Continuous Discretely
• Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series
• On Barnes' multiple zeta and gamma functions

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