Lower Bounds on the number of rational points of Jacobians over finite fields and application to algebraic function fields in towers.
2015
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 $r\leq g$. 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-Vladut invariants.
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