Narrow Results

We consider the arithmetic background of integral representations of finite groups over $p$-adic and algebraic number rings. Some infinite series of integral pairwise inequivalent absolutely irreducible representations of finite $p$-groups with the extra congruence conditions are constructed, and some applications are given. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed.

Let $K/F$ be a quadratic tamely ramified extension of a non-Archimedean local field $F$ of characteristic zero. In this paper, we give an explicit formula for Langlands’ lambda function ${\lambda }_{K/F}$.