Lower bounds for the class number of an algebraic function field over a finite field (Q639575)

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 \(B_r\).