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
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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