Titlebook: Elliptic Curves, Modular Forms and Cryptography; Proceedings of the A Ashwani K. Bhandari,D. S. Nagaraj,T. N. Venkataram Conference proceed

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The Mordell-Weil Theoremoup. In other words, .(.) ? ?. ⊕ . where . is a finite abelian group, the torsion subgroup. One refers to .(.) as the Mordell-Weil group of . over .. Geometrically, if one is given a system of generators for .(.), then one can produce all the points by the chord and tangent process. This means that

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Erythropoietin

-adic Theta Functions and Tate Curvesthe theory of .-adic theta functions. The exposition mainly follows ([Hus86], Chapter 10), The final section illustrates an application of these ideas by giving Serre’s proof of the Tate conjectures for Tate curves. It is based on ([Ser68], Chapter 4).

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Entirety

Introductionse branches of Mathematics coming together in the theory of Elliptic Curves and Modular Forms to solve one of the outstanding problems in Number Theory, viz., ‘The Fermat’s Last Theorem’. In Part I of this volume, various aspects of the theory of Elliptic Curves are given. In Part II, we discuss som

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