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Elementary and analytic theory of algebraic numbers
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In this paper, Dedekind Domains and Valuations have been used to define the theory of P-adic fields and to define a local compact Abelian group. But they do not consider the relation between the two types of fields.Abstract:
1. Dedekind Domains and Valuations.- 2. Algebraic Numbers and Integers.- 3. Units and Ideal Classes.- 4. Extensions.- 5. P-adic Fields.- 6. Applications of the Theory of P-adic Fields.- 7. Analytical Methods.- 8. Abelian Fields.- 9. Factorizations 9.1. 485Elementary Approach.- Appendix I. Locally Compact Abelian Groups.- Appendix II. Function Theory.- Appendix III. Baker's Method.- Problems.- References.- Author Index.- List of Symbols.read more
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Deforming Galois Representations
TL;DR: In this paper, the Galois group of the maximal algebraic extension of ℚ unramified outside the finite set S of primes of the continuous homomorphism ρ to p-adic representations is studied.
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Classical and modular approaches to exponential Diophantine equations. I. Fibonacci and Lucas perfect powers
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Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers
TL;DR: In this paper, the authors combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's last theorem.
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The determination of Gauss sums
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Fake projective planes
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