The two-variable zeta function and the Riemann hypothesis for function fields

DOI10.1016/j.exmath.2007.11.001zbMath1213.11163arXiv0806.0044OpenAlexW2035885871MaRDI QIDQ935410

Machiel van Frankenhuijsen

Publication date: 6 August 2008

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.0044

zbMATH Keywords

Riemann hypothesis for a curve over a finite fieldtwo-variable zeta functionzeta function of a curve over a finite field

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Zeta and (L)-functions in characteristic (p) (11M38)

Cites Work

• Unnamed Item
• Algebraic function fields and codes
• On the irreducibility of the two variable zeta-function for curves over finite fields.
• Basic number theory.
• ON THE NUMBER OF POINTS OF A HYPERELLIPTIC CURVE OVER A FINITE PRIME FIELD
• Numbers of solutions of equations in finite fields