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Summation Formulae for Coefficients of L-functions

Published online by Cambridge University Press:  20 November 2018

John B. Friedlander
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, M5S 3G3, e-mail: [email protected]
Henryk Iwaniec
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, U.S.A. and Courant Institute of Mathematical Sciences, NYU, New York, NY 10012, U.S.A.
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Abstract

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With applications in mind we establish a summation formula for the coefficients of a general Dirichlet series satisfying a suitable functional equation. Among a number of consequences we derive a generalization of an elegant divisor sum bound due to F. V. Atkinson.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2005

References

[A] Atkinson, F. V., A divisor problem. Quart. J. Math. (Oxford) 12(1941) 193–200.Google Scholar
[FI] Friedlander, J. B. and Iwaniec, H., Exceptional zeros and prime numbers in short intervals. Selecta Math. (N.S.) 10(2004), 6169.Google Scholar
[GK] Graham, S.W. and Kolesnik, G., Van der Corput's Method of Exponential Sums. London Mathematical Society Lecture Note Series 126, Cambridge University Press, Cambridge, 1991.Google Scholar
[K] Kolesnik, G., On the estimation of multiple exponential sums. In: Recent Progress in Analytic Number Theory I, Academic Press, London, 1981, pp. 231–246,Google Scholar
[MS] Miller, S. D. and Schmid, W., Summation formulas, from Poisson and Voronoi to the present. In: Noncommutative harmonic analysis. Progr.Math. 220, Birkhäusser, Boston, 2003, pp. 419440.Google Scholar
[T] Titchmarsh, E. C., The Theory of the Riemann Zeta-function. 2nd edition, The Clarendon Press, Oxford, 1986.Google Scholar