- Series: Graduate Texts in Mathematics (Book 97)
- Hardcover: 252 pages
- Publisher: Springer; 2nd edition (April 29, 1993)
- Language: English
- ISBN-10: 0387979662
- ISBN-13: 978-0387979663
- Product Dimensions: 6.1 x 0.6 x 9.2 inches
- Shipping Weight: 15.2 ounces (View shipping rates and policies)
- Average Customer Review: 6 customer reviews
- Amazon Best Sellers Rank: #898,540 in Books (See Top 100 in Books)
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Introduction to Elliptic Curves and Modular Forms (Graduate Texts in Mathematics) 2nd Edition
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About the Author
Neal Koblitz is a Professor of Mathematics at the University of Washington in the Department of Mathematics. He is also an adjunct professor with the Centre for Applied Cryptographic Research at the University of Waterloo. He is the creator of hyperelliptic curve cryptography and the independent co-creator of elliptic curve cryptography. Professor Koblitz received his undergraduate degree from Harvard University, where he was a Putnam Fellow, in 1969. He received his Ph.D. from Princeton University in 1974 under the direction of Nickolas Katz.
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The book is divided into four major sections. The first, quite interestingly, develops the theory of elliptic curves starting from congruent numbers. The discussion on elliptic functions, the Weierstrass form, etc are all very nicely done. The second section involves looking at the Hasse-Weil L-function of an elliptic curve. The discussion on the Riemann zeta function and the functional equation of the Hasse-Weil L-function were very informative and easy to understand, without sacrificing rigour. The last two sections deal with modular forms. The first of the two involves studying the SL(2,Z) group, developing modular forms for this group and a brief discussion of theta functions and Hecke operators. The last section is in many ways the most interesting, dealing with modular forms of half-integer weight and finishing with the theorems by Shimura, Tunnell, etc.
For a book that is barely 200 pages long, there is a good range of topics covered, and the presentation is very elegant. The book maintains a high standard of rigour throughout and deserves all the praise that it has rightfully earned. My only crib, and it is a minor one, is that the transition from elliptic curves to modular forms is not an entirely seamless one.