An explicit regular PSp(2,3)-polynomial over Q(\sqrt{-3}) Hidetaka Kitayama (Osaka University) The inverse Galois problem asks whether there exists a G-extension over K for a given field K and a finite group G. This problem has been studied by many mathematicians as one of the most important problems in number theory, especially for the case of the rational number field Q. It is still unknown whether the problem admits an affirmative answer for every finite group, but it has been proven to do so for a lot of finite groups. We will consider constructive aspects of the inverse Galois problem. In this talk, we will consider PSp(2,3)-extensions by using some results of Siegel modular forms, and give explicitly a regular PSp(2,3)-polynomial over Q(\sqrt{-3}) with 3 parameters of degree 40.