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Let C be a (non-singular, projective, geometrically irreducible, algebraic) curve of genus g defined over a finite field F q with q elements. We know after A. Weil that the number of F q-points of a curve of genus g defined over F q satisfies the following limitations: q + 1 − 2g √ q ≤ #C(F q) ≤ 1 + q + 2g √ q, where C(F q) denotes the set of F q-rational… (More)

Asymptotics for the genus and the number of rational places in towers of function fields over a finite field Abstract We discuss the asymptotic behaviour of the genus and the number of rational places in towers of function fields over a finite field.

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