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

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

1999-03-21

arxiv.org/abs/math/9903195v1

Mathematics

Number Theory

Scientific paper

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.

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