Let E be a cyclic algebraic number eld of a prime degree. We prove an identity which lifts an exponential sum similar to the Kloosterman sum to an exponential sum taken over certain algebraic integers in E.

Let E be a cyclic algebraic number field of prime degree. We prove an identity which lifts an exponential sum similar to the Kloosterman sum to an exponential sum taken over certain algebraic integers in E.

Let $\overline{\mathbb Q}$ be an algebraic closure of $\mathbb Q$ and let Z}$ denote the ring integers in Q}$. If $\mathcal V = \overline{\mathbb Q}^\times /\overline{\mathbb Z}^\times $ then V$

We give an overview of universal quadratic forms and lattices, focusing on the recent developments over rings integers in totally real number fields. In particular, we discuss indecomposable algebraic as one main tools.