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Download E-books Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library) PDF

Many difficulties in quantity concept have basic statements, yet their recommendations require a deep knowing of algebra, algebraic geometry, advanced research, workforce representations, or a mix of all 4. the unique easily said challenge should be obscured within the intensity of the idea constructed to appreciate it. This e-book is an advent to a couple of those difficulties, and an summary of the theories used these days to assault them, awarded in order that the quantity idea is usually on the vanguard of the dialogue. Lozano-Robledo offers an introductory survey of elliptic curves, modular kinds, and $L$-functions. His major aim is to supply the reader with the massive photo of the mind-blowing connections between those 3 households of mathematical gadgets and their which means for quantity concept. As a working example, Lozano-Robledo explains the modularity theorem and its well-known outcome, Fermat's final Theorem. He additionally discusses the Birch and Swinnerton-Dyer Conjecture and different glossy conjectures. The e-book starts off with a few motivating difficulties and comprises a number of concrete examples through the textual content, usually related to real numbers, similar to three, four, five, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular kinds, and $L$-functions are too mammoth to be coated in one quantity, and their proofs are open air the scope of the undergraduate curriculum. even if, the first gadgets of analysis, the statements of the most theorems, and their corollaries are in the take hold of of complicated undergraduates. This publication concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and supplying plenty of examples, instead of residing at the tough proofs. The booklet succeeds if, after analyzing the textual content, scholars consider pressured to check elliptic curves and modular kinds in all their glory.

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