Elliptic Curves: Function Theory, Geometry, Arithmetic by Henry McKean and Victor Moll offers a comprehensive introduction to one of mathematics’ most profound subjects. Bridging analysis, geometry, and number theory, this text presents elliptic curves as a unifying theme in modern mathematics.
Key Features:
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Interdisciplinary Approach: Connects complex analysis, algebraic geometry, and number theory through elliptic curves
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Function-Theoretic Foundations: Covers Weierstrass ℘function, modular forms, and theta functions
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Arithmetic Applications: Includes rational points, Mordell-Weil theorem, and connections to Fermat’s Last Theorem
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Geometric Insights: Explores the group law, isogenies, and complex multiplication
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Computational Aspects: Provides concrete examples and exercises throughout
This graduate-level text serves as an ideal preparation for advanced topics in:
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Modern cryptography (ECC)
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Langlands program
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Modularity theorems
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Diophantine geometry
Why This Book Stands Out:
McKean and Moll’s distinctive style combines rigorous mathematics with insightful commentary, making deep results accessible. The treatment emphasizes the beautiful interplay between analysis (“function theory”) and arithmetic, offering readers a panoramic view of elliptic curves.
Perfect For:
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Graduate students in number theory
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Researchers in algebraic geometry
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Mathematical physicists studying integrable systems
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Cryptography specialists exploring ECC foundations
