The [formula omitted]-Iwasawa theory

Abstract

Iwasawa made the fundamental discovery that there is a close connection between the ideal class groups of Zp-extensions of cyclotomic fields and the p-adic analogue of Riemann's zeta functionsζ(s)=∑n=1∞1ns. In this paper, we show that there may also exist a parallel Iwasawa's theory corresponding to the p-adic analogue of Euler's deformation of zeta functionsϕ(s)=∑n=1∞(−1)n−1ns.