By Haruzo Hida

This booklet features a distinctive account of the results of the author's contemporary Annals paper and JAMS paper on mathematics invariant, together with μ-invariant, L-invariant, and related topics.   This publication might be considered as an introductory textual content to the author's prior e-book p-Adic Automorphic varieties on Shimura Varieties.  Written as a down-to-earth creation to Shimura forms, this article comprises many examples and purposes of the speculation that offer motivation for the reader.  because it is restricted to modular curves and the corresponding Shimura types, this booklet isn't just an exceptional source for specialists within the box, however it is additionally obtainable to complex graduate scholars learning quantity theory.  Key issues contain non-triviality of mathematics invariants and distinctive values of L-functions; elliptic curves over advanced and p-adic fields; Hecke algebras; scheme idea; elliptic and modular curves over jewelry; and Shimura curves.

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