On quotients of Riemann zeta values at odd and even integer arguments

@article{Kellner2013OnQO,
  title={On quotients of Riemann zeta values at odd and even integer arguments},
  author={Bernd C. Kellner},
  journal={Journal of Number Theory},
  year={2013},
  volume={133},
  pages={2684-2698}
}
Abstract We show for even positive integers n that the quotient of the Riemann zeta values ζ ( n + 1 ) and ζ ( n ) satisfies the equation ζ ( n + 1 ) ζ ( n ) = ( 1 − 1 n ) ( 1 − 1 2 n + 1 − 1 ) L ⋆ ( p n ) p n ′ ( 0 ) , where p n ∈ Z [ x ] is a certain monic polynomial of degree n and L ⋆ : C [ x ] → C is a linear functional, which is connected with a special Dirichlet series. There exists the decomposition p n ( x ) = x ( x + 1 ) q n ( x ) . If n = p + 1 where p is an odd prime, then q n is an… Expand
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Über das Eulersche Summierungsverfahren