A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function
Acta Arithmetica, Tome 158 (2013) no. 1, pp. 1-31
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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 $\zeta (2s)$ and some seemingly new Bernoulli relations, which we use to obtain a generalised Ramanujan polynomial and properties thereof.
Keywords:
study interplay between recurrences zeta related functions integer values minor corner lattice toeplitz determinants integer composition based sums investigations touch functional identities due ramanujan grosswald transcendence zeta function odd integer values criterion riemann hypothesis pseudo characteristic polynomials zeta related functions begin recent result zeta seemingly bernoulli relations which obtain generalised ramanujan polynomial properties thereof
Affiliations des auteurs :
M. C. Lettington 1
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author = {M. C. Lettington},
title = {A trio of {Bernoulli} relations, their implications for the {Ramanujan} polynomials and the special values of the {Riemann} zeta function},
journal = {Acta Arithmetica},
pages = {1--31},
year = {2013},
volume = {158},
number = {1},
doi = {10.4064/aa158-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa158-1-1/}
}
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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, Tome 158 (2013) no. 1, pp. 1-31. doi: 10.4064/aa158-1-1
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