منابع مشابه
The Hasse–Minkowski Theorem
The Hasse-Minkowski Theorem provides a characterization of the rational quadratic forms. What follows is a proof of the Hasse-Minkowski Theorem paraphrased from the book, Number Theory by Z.I. Borevich and I.R. Shafarevich [1]. Throughout this paper, some familiarity with the p-adic numbers and the Hilbert symbol is assumed and some basic facts about quadratic forms are stated without proof. Al...
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For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field.
متن کاملSome Remarks on the Hasse-Arf Theorem
We give a very simple proof of Hasse-Arf theorem in the particular case where the extension is Galois with an elementary-abelian Galois group of exponent p. It just uses the transitivity of different exponents and Hilbert’s different formula. Let E/F be a finite Galois extension with Galois group G = Gal(E/F ). Let P be a place of F and let Q be a place of E lying above P . We assume that the c...
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توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولDavenport-Hasse theorem and cyclotomic association schemes
Definition. Let q be a prime power and e be a divisor of q − 1. Fix a generator α of the multiplicative group of GF (q). Then 〈α〉 is a subgroup of index e and its cosets are 〈α〉α, i = 0, . . . , e− 1. Define R0 = {(x, x)|x ∈ GF (q)} Ri = {(x, y)|x, y ∈ GF (q), x− y ∈ 〈αe〉αi−1}, (1 ≤ i ≤ e) R = {Ri|0 ≤ i ≤ e} Then (GF (q),R) forms an association scheme and is called the cyclotomic scheme of clas...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1975
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1975-13746-3