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Lower bounds for the class number of an algebraic function field over a finite field. (Minorations du nombre de classes des corps de fonctions algébriques définis sur un corps fini.) (French) Zbl 1239.11131

Let \(F\) be a function field of one variable defined over a finite field \(\mathbb F_q\) and having genus \(g\). Let \(r\geq 1\) and let \(B_1\) and \(B_r\) be the number of places of \(F\) of degrees 1 and \(r\). Assume that \(B_1>0\) and \(B_r>0\). Let \(h\) be the class number of \(F\) over \(\mathbb F_q\). The paper gives lower bounds for the number of effective divisors of degree less than \(g\) and gives lower bounds for \(h\), each in terms of \(B_1\) and \(B_r\).

MSC:

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

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