# Moscow Mathematical Journal

Volume 15, Issue 3, July–September 2015 pp. 425–433.

Lower Bounds on the Number of Rational Points of Jacobians over Finite Fields and Application to Algebraic Function Fields in Towers

**Authors**:
S. Ballet (1), R. Rolland (1), and S. Tutdere (2)

**Author institution:**(1) Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France, case 907, 163 Avenue de Luminy, 13288 Marseille Cedex 9

(2) Department of Mathematics, Gebze Institute of Technology, Gebze, Kocaeli, Turkey

**Summary: **

We give effective bounds on the class number of any algebraic function field of genus *g* defined over a finite field. These bounds
depend on the possibly partial information on the number of places on
each degree *r*≤*g*. Such bounds are especially useful for estimating the
class numbers of function fields in towers of function fields over finite
fields having several positive Tsfasman–Vlăduţ invariants.

2010 Math. Subj. Class. Primary: 14H05; Secondary: 12E20.

**Keywords:**Finite field, Jacobian, algebraic function field, class number, tower.

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