Zeta functions and basic analogues

Date

2010-11-10T20:06:29Z

Authors

Anderson, Peter John

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Abstract

We present results evolving from established connections between zeta functions and different systems of polynomials, particularly the Riemann and Hurwitz zeta functions and the Bernoulli and Euler polynomials. In particular we develop certain results related to Apostol's deformation of the Bernoulli polynomials and obtain identities of Carlitz by a novel approach using generating functions instead of difference equations. In the last two chapters we work out new rapidly convergent series expansions of the Riemann zeta function, find coefficient symmetries of a polynomial sequence obtained from the cyclotomic polynomials by a linear fractional transformation of argument and obtain an expression for the constant term in an identity involving the gamma function.

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Keywords

zeta functions, number theory

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