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Comment on the sums
-
Zurab Silagadze
Published/Copyright:
September 18, 2012
Abstract.
This is a comment on the papers from Elkies [Amer. Math. Monthly 110 (2003), 561–573] and
Cvijović–Klinowski [J. Comput. Appl. Math. 142 (2002), 435–439].
We provide an explicit expression for
the kernel of the integral operator introduced in Elkies' paper. This
explicit expression considerably simplifies the calculation of 
and
enables a simple derivation of Cvijović and Klinowski's integral
representation for 
.
Keywords: Riemann zeta function; integral representation
Received: 2011-06-13
Published Online: 2012-09-18
Published in Print: 2012-09-01
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- The Plemelj–Privalov theorem in variable exponent Clifford analysis
- Almost everywhere convergence of a subsequence of logarithmic means of Fourier series on the group of 2-adic integers
- Identities and generating functions on Chebyshev polynomials
- Left annihilators of power values of commutators with generalized derivations
- On various classes of bitopological spaces
- On P-torsion modules over a pullback of two Dedekind domains
- A remark on a polynomial matrix factorization theorem
- Convergence of double Fourier series and generalized Λ-variation
- On monoids of monotone injective partial selfmaps of integers with cofinite domains and images
- On the boundedness of product kernel operators with measures
- A new class of generalized Hermite–Bernoulli polynomials
- Global nonexistence and stability of solutions of inverse problems for a class of Petrovsky systems
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