Refined asymptotics of the Riemann-Siegel theta function

R. B. Paris*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    35 Downloads (Pure)


    The Riemann-Siegel theta function ϑ(t) is examined for t → +∞. Use
    of the refined asymptotic expansion for log Γ(z) shows that the expansion of ϑ(t)
    contains an infinite sequence of increasingly subdominant exponential terms, each
    multiplied by an asymptotic series involving inverse powers of πt. Numerical examples are given to detect and confirm the presence of the first three of these exponentials.
    Original languageEnglish
    Pages (from-to)17-27
    Number of pages11
    JournalBulletin of Kerala Mathematics Association
    Issue number2
    Early online date1 Dec 2020
    Publication statusPublished - 1 Dec 2020


    • Riemann-Siegel theta function
    • Gamma function
    • Asymptotic expansion
    • Stokes phenomenon


    Dive into the research topics of 'Refined asymptotics of the Riemann-Siegel theta function'. Together they form a unique fingerprint.

    Cite this