Small Values of |L'/L(1,χ)|

Abstract

In this article, we investigate the quantity , as over the primes, where is the Dirichlet L-function attached to a non-principal Dirichlet character modulo q. Our main result shows that . We also compute mq for every odd prime q up to 10. As a consequence we numerically verified that for every prime q, , we have , with . In particular, this shows that for every non-principal Dirichlet character χ mod q where is prime, answering a question of Gun, Murty and Rath in this range. We also provide some statistics and scatter plots regarding the mq-values. The programs used and the computational results described here are available at the following web address: https://www.math.unipd.it/~languasc/smallvalues.html.