English

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

Number Theory 2016-09-07 v1

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 Andr\'e 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.

Cite

@article{arxiv.math/9903195,
  title  = {A residue scalar product for algebraic function fields over a number field},
  author = {Xian-Jin Li},
  journal= {arXiv preprint arXiv:math/9903195},
  year   = {2016}
}