Titlebook: Iwasawa Theory 2012; State of the Art and Thanasis Bouganis,Otmar Venjakob Conference proceedings 2014 Springer-Verlag Berlin Heidelberg 20

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Contributions in Mathematical and Computational Scienceshttp://image.papertrans.cn/i/image/476608.jpg

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Iwasawa ,-Invariants of ,-Adic Hecke ,-FunctionsThis article surveys recent developments on Iwasawa .-invariants of .-adic Hecke .-functions for CM fields following Hida.

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Nearly Overconvergent Modular FormsWe introduce and study finite slope nearly overconvergent (elliptic) modular forms. We give an application of this notion to the construction of the Rankin-Selberg .-adic L-function on the product of two eigencurves..

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On ,-Zeta FunctionWe present in this note a definition of zeta function of the field . which incorporates all .-adic L-functions of Kubota-Leopoldt for all . and also so called Soulé classes of the field .. This zeta function is a measure, which we construct using the action of the absolute Galois group . on fundamental groups.

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The Structure of Selmer Groups of Elliptic Curves and Modular Symbolshe main conjecture nor the non-degeneracy of the .-adic height pairing, and study the structure of Selmer groups (see Theorems . and .), using these analytic elements and Kolyvagin systems of Gauss sum type.

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Conference proceedings 2014 different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory..Iwasawa theory is a modern and powerful b

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