A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function

• Autorzy: M. C. Lettington
• Języki publikacji: EN

Abstrakty

EN

We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli relations, which we use to obtain a generalised Ramanujan polynomial and properties thereof.

Kategorie tematyczne

• 11B68: Bernoulli and Euler numbers and polynomials
• 11S05: Polynomials
• 11J81: Transcendence (general theory)
• 11C20: Matrices, determinants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 1
• Strony: 1-31

Daty

wydano

2013

Twórcy

autor

M. C. Lettington

• School of Mathematics, Cardiff University, P.O. Box 926, Cardiff CF24 4AG, UK

Identyfikatory

DOI

10.4064/aa158-1-1