THUE-VINOGRADOV AND INTEGERS OF THE FORM x +Dy
نویسنده
چکیده
Introduction – Study of an Elementary Proof 1 1. The Lemmas of Thue and Vinogradov 4 2. Preliminaries on Quadratic Reciprocity and Quadratic Forms 4 2.1. Quadratic reciprocity law 4 2.2. Binary quadratic forms 5 3. Thue-Vinogradov Applied to Binary Quadratic Forms 7 4. First Applications of Theorem 9 8 4.1. Indefinite forms 8 4.2. Positive definite forms 10 5. Primes of the form x +Dy for idoneal D 12 5.1. Auxiliary Congruence Conditions and Small Examples 12 5.2. The representation theorem 13 5.3. Preparatory Lemmas 14 5.4. Proof of the Representation Theorem: D ≡ 1, 5 (mod 8) 15 5.5. Proof of the Representation Theorem: D ≡ 2, 6 (mod 8) 16 5.6. Proof of the Representation Theorem: D ≡ 3, 7 (mod 8) 17 5.7. Proof of the Representation Theorem: D ≡ 4 (mod 8) 17 5.8. Proof of the Representation Theorem: D ≡ 0 (mod 8) 18 6. Some representations of squarefree integers 19 6.1. A squarefree representation theorem 19 6.2. Further background on quadratic forms 21 6.3. The proof of Theorem 34 21 References 23
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