the arithmetic of elliptic curves 2nd edition by joseph h silverman pdf xyur

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==> the arithmetic of elliptic curves 2nd edition by joseph h silverman pdf <==

"The Arithmetic of Elliptic Curves" (2nd edition) by Joseph H. Silverman is a comprehensive text that explores the theory and applications of elliptic curves, which are fundamental objects in algebraic geometry and number theory. The book covers the arithmetic properties of elliptic curves over various fields, including the rational numbers, and examines their connections to modular forms and Diophantine equations. Silverman provides a clear and detailed introduction to the subject, making it accessible to graduate students while also serving as a valuable reference for researchers. The second edition includes updates and new material that reflect recent developments in the field, such as advances in the Birch and Swinnerton-Dyer conjecture. Through a mix of theoretical insights and practical examples, Silverman aims to delve into both the foundational aspects and the ultimate implications of elliptic curves in modern mathematics, emphasizing their significance in cryptography and coding theory. Overall, this book is an essential resource for anyone looking to deepen their understanding of elliptic curves and their rich interplay with various areas of mathematics.