Nonsolvable number fields ramified only at 3 and 5

TL;DR

This paper constructs explicit examples of finite nonsolvable number fields ramified only at 3 and 5 using computations with Hilbert modular forms, advancing understanding of ramification in number theory.

Contribution

It provides explicit constructions of nonsolvable number fields ramified only at specific primes, a novel achievement in the explicit realization of such fields.

Findings

Explicit examples of nonsolvable ramified fields at 3 and 5.

Use of Hilbert modular forms for field construction.

Advancement in understanding ramification constraints.

Abstract

For p = 3 and p = 5, we exhibit a finite nonsolvable extension of the rational numbers which is ramified only at p via explicit computations with Hilbert modular forms.