Riemann surfaces of genus $1+q^2$ with $3q^2$ automorphisms

Abstract

In this article we classify compact Riemann surfaces of genus $1+q^2$ with a group of automorphisms of order $3q^2,$ where $q$ is a prime number. We also study decompositions of the corresponding Jacobian varieties.

arXiv comment26 pages, A small mistake in Th. 2 is amended