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

M. C. Lettington. "A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function." Acta Arithmetica 158.1 (2013): 1-31. <http://eudml.org/doc/279587>.

@article{M2013,
abstract = {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.},
author = {M. C. Lettington},
journal = {Acta Arithmetica},
keywords = {Ramanujan polynomials; Bernoulli relations; Riemann zeta function},
language = {eng},
number = {1},
pages = {1-31},
title = {A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function},
url = {http://eudml.org/doc/279587},
volume = {158},
year = {2013},
}

TY - JOUR
AU - M. C. Lettington
TI - A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function
JO - Acta Arithmetica
PY - 2013
VL - 158
IS - 1
SP - 1
EP - 31
AB - 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.
LA - eng
KW - Ramanujan polynomials; Bernoulli relations; Riemann zeta function
UR - http://eudml.org/doc/279587
ER -