On the Riemann–Siegel formula

DOI10.1098/rspa.2007.1888zbMath1133.11050OpenAlexW2095627247MaRDI QIDQ5438434

Alexey Kuznetsov

Publication date: 23 January 2008

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2007.1888

zbMATH Keywords

Riemann zeta functionasymptotic expansionincomplete gamma-functionRiemann-Siegel formula

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Analytic computations (11Y35)

Cites Work

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• On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function
• The definite integral \(\int_{-\infty}^\infty {e^{ax^2+bx}\over e^{cx+d}}dx\) and the analytic theory of numbers
• A new asymptotic representation for ζ(½ + i t ) and quantum spectral determinants
• The Asymptotic Expansion of the Incomplete Gamma Functions
• An asymptotic representation for the Riemann zeta function on the critical line
• Integral representations for the Dirichlet L-functions and their expansions in Meixner–Pollaczek polynomials and rising factorials†

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