New lower bounds for the Ihara function A(q)A(q) for small primes

The Ihara function, A(q)A(q), is an asymptotic measure comparing the number of rational places of a global function field with its genus. In this paper, we improve the best known lower bounds for A(7)A(7) and A(11)A(11) and match the best known lower bound for A(13)A(13).