## Abstract

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.

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 language | English |
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Pages (from-to) | 17-27 |

Number of pages | 11 |

Journal | Bulletin of Kerala Mathematics Association |

Volume | 16 |

Issue number | 2 |

Early online date | 1 Dec 2020 |

Publication status | Published - 1 Dec 2020 |

## Keywords

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