By Haruzo Hida

This e-book encompasses a targeted account of the results of the author's fresh Annals paper and JAMS paper on mathematics invariant, together with μ-invariant, L-invariant, and comparable topics.   This booklet may be considered as an introductory textual content to the author's prior e-book p-Adic Automorphic types on Shimura Varieties.  Written as a down-to-earth creation to Shimura kinds, this article contains many examples and functions of the speculation that supply motivation for the reader.  because it is proscribed to modular curves and the corresponding Shimura forms, this publication isn't just an exceptional source for specialists within the box, however it can be obtainable to complex graduate scholars learning quantity theory.  Key issues comprise non-triviality of mathematics invariants and specific values of L-functions; elliptic curves over complicated and p-adic fields; Hecke algebras; scheme conception; elliptic and modular curves over earrings; and Shimura curves.

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