The (S,{2})-Iwasawa theory

Abstract

Iwasawa made the fundamental discovery that there is a close connection between the ideal class groups of ${\mathbb{Z}}_p$-extensions of cyclotomic fields and the $p$-adic analogue of Riemann's zeta functions $$\zeta (s)=\sum _{n=1}^{\infty }\frac{1}{n^s}.$$ 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 functions $$\varphi (s)=\sum _{n=1}^{\infty }\frac{(-1{)}^{n-1}}{n^s}.$$

arXiv comment15 Pages