A residue scalar product for algebraic function fields over a number field

1999/03/21 by Xian‐Jin Li, Li, Xian-Jin
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/9903195

openalex publication_date 1999/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1952 Peter Roquette gave an arithmetic proof of the Riemann hypothesis for algebraic function fields of a finite constants field, which was proved by André Weil in 1940. The construction of Weil's scalar product is essential in Roquette's proof. In this paper a scalar product for algebraic function fields over a number field is constructed which is the analogue of Weil's scalar product.

Citations

• The Positivity of a Sequence of Numbers and the Riemann Hypothesis

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