Displaying similar documents to “Exploring the q -Riemann zeta function and q -Bernoulli polynomials.”

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

M. C. Lettington (2013)

Acta Arithmetica

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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...

A zero density result for the Riemann zeta function

Habiba Kadiri (2013)

Acta Arithmetica

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We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.