Abstract
In this note we establish two theorems concerning asymptotic expansion of Riemann-Siegel integrals as well as formula of generating function (double series) of coefficents of that expansion (for computation aims); we also discuss similar results for Dirichlet series (L(s, fh) and L(s,X)), with m odd integer and X(n)(mod(m)) (even) primitive characters (inappendixB).
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References
Titchmarsh, E. C., (a) The Theory of the Functions. Oxford University Press, 1952. (b) The Theory of the Riemann Zeta Function, 1951.
Edwards, H. M., The Riemann's Zeta Function, 1974.
Karachuba, A. A., Foundation of Analytic Number Theory, (Chinese Translation), Adademic Press, 1984.
Wang Z. X. and Guo D. R., Theory of Special Functions (In Chinese), Academic Press, Beijing, 1965.
Hua, L. G., Introduction to Number Theory (In Chinese), Academic Press, Beijing, 1956.
Levinson, N., More than One Third of Zeros of Riemann's Zeta Function Are on σ = 1/2, Adv. in Math., 13(1974), 383–436.
Deuring, M., Asymptotic Entwicklungen der Dirichletschen L-Reihen, Math. Annalen, 168(1967), 1–30.
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This paper is that of a talk on the ≪International Conference at Analysis in Thory and Applications≫ held in Nanjing, P. R. China, July, 2004.
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Chen, G. Note on asymptotic expansion of Riemann-Siegel integral. Analysis in Theory and Applications 22, 120–135 (2006). https://doi.org/10.1007/BF03218705
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DOI: https://doi.org/10.1007/BF03218705
Key words
- Riemann-Siegel integral
- asymptotic expansion
- asymptotic functional equation
- Binet
- formula
- Titchmarsh technique