On the number of rational points of Jacobians over finite fields

• Autorzy: Philippe Lebacque , Alexey Zykin
• Języki publikacji: EN

Abstrakty

EN

We prove lower and upper bounds for the class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in the proof are essentially those from the explicit asymptotic theory of global fields. We thus provide a concrete application of effective results from the asymptotic theory of global fields and their zeta functions.

Kategorie tematyczne

• 11R29: Class numbers, class groups, discriminants
• 11R58: Arithmetic theory of algebraic function fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 169
• Numer: 4
• Strony: 373-384

Daty

wydano

2015

Twórcy

autor

Philippe Lebacque

• Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16, route de Gray, 25030 Besançon Cedex, France
• Inria Saclay-Ile-de-France, équipe-projet Grace

autor

Alexey Zykin

• Laboratoire GAATI, Université de la Polynésie française, BP 6570 98702 Faa'a, Tahiti, French Polynesia
• National Research University, Higher School of Economics, AG Laboratory, HSE, 7 Vavilova St., Moscow 117312, Russia
• Laboratoire Poncelet (UMI 2615), Russian Academy of Sciences
• Institute for Information Transmission Problems, Russian Academy of Sciences

Identyfikatory

DOI

10.4064/aa169-4-5