On Jacobi Sums in $\mathbb Q(\zeta_p)$

TL;DR

This paper investigates the p-adic properties of Jacobi sums in cyclotomic fields and explores their connection to the structure of the p-Sylow subgroup of the class group of the maximal real subfield.

Contribution

It provides new insights into the p-adic behavior of Jacobi sums and establishes a link to the class group structure in cyclotomic fields.

Findings

p-adic properties of Jacobi sums are characterized

Connection between Jacobi sums and class group p-Sylow subgroups is demonstrated

Results contribute to understanding cyclotomic field arithmetic

Abstract

We study the p-adic behavior of Jacobi Sums for $\mathbb Q(\zeta_p)$ and link this study to the p-Sylow subgroup of the ideal class group of $\mathbb Q(\zeta_p\`a^+$