Riemann operators on higher $K$-groups

TL;DR

This paper introduces Riemann operators on higher algebraic K-groups of number rings and shows their determinants relate to gamma factors of Dedekind zeta functions, linking algebraic K-theory with number theory.

Contribution

It defines Riemann operators on higher K-groups and establishes their connection to the gamma factors of Dedekind zeta functions, providing a new analytical tool.

Findings

Gamma factors are obtained as regularized determinants of Riemann operators.

Riemann operators act on Quillen's higher K-groups of number rings.

The work bridges algebraic K-theory and analytic number theory.

Abstract

We introduce Riemann operators acting on Quillen's higher $K$--groups $K_{n}(A)$ for the integer ring $A$ of an algebraic number field $K$. Especially we prove that gamma factors of Dedekind zeta function of $K$ are obtained as regularized determinants of Riemann operators.