© 2013

Elliptic Curves and Arithmetic Invariants


Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Haruzo Hida
    Pages 43-82
  3. Haruzo Hida
    Pages 145-216
  4. Haruzo Hida
    Pages 217-224
  5. Haruzo Hida
    Pages 225-279
  6. Haruzo Hida
    Pages 281-334
  7. Haruzo Hida
    Pages 335-365
  8. Haruzo Hida
    Pages 387-403
  9. Back Matter
    Pages 427-449

About this book


This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics.   This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties.  Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader.  Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory.  Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.


Hecke algebra Shimura variety arithmetic invariants elliptic curves modular forms scheme theory

Authors and affiliations

  1. 1.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA

About the authors

Haruzo Hida is currently a professor of mathematics at University of California, Los Angeles.

Bibliographic information

  • Book Title Elliptic Curves and Arithmetic Invariants
  • Authors Haruzo Hida
  • Series Title Springer Monographs in Mathematics
  • Series Abbreviated Title Springer Monographs in Mathematics
  • DOI
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4614-6656-7
  • Softcover ISBN 978-1-4899-9092-1
  • eBook ISBN 978-1-4614-6657-4
  • Series ISSN 1439-7382
  • Edition Number 1
  • Number of Pages XVIII, 450
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    Algebraic Geometry
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking


“The main aim of the book is to give an account of Hida’s results on arithmetic invariants in an accessible way. … The book is intended for mathematicians with some background on modular forms and is worthwhile for both graduate students and experts. … There are numerous examples, exercises, and remarks, all aimed at carefully helping the reader. In conclusion, this book is a very welcome addition to the mathematical literature.” (Florian Sprung, Mathematical Reviews, April, 2015)

“The author gives in this book a detailed account of results concerning arithmetic invariants, including µ-invariant and L-invariant. … it contains a detailed account of the author’s recent results concerning arithmetic invariants. The book, addressed to advanced graduate students and experts working in number theory and arithmetic geometry, is a welcome addition to this beautiful and difficult area of research.” (Andrzej Dąbrowski, zbMATH, Vol. 1284, 2014)