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arXiv · 1310.4257

The (S,{2})-Iwasawa theory

Su Hu·Min-Soo Kim
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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 $$\phi(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^{s}}.$$

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Su Hu, Min-Soo Kim. 2013-10-16. The (S,{2})-Iwasawa theory. https://arxiv.org/abs/1310.4257

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