Construction of certain real quadratic fields
نویسندگان
چکیده
منابع مشابه
Quadratic Residue Covers for Certain Real Quadratic Fields
Let A„{a, b) = {ban+(a-l)/b)2+4an with n > 1 and ¿>|a-l . If W is a finite set of primes such that for each n > 1 there exists some q £W for which the Legendre symbol {A„{a, b)/q) ^ -1 , we call <£ a quadratic residue cover (QRC) for the quadratic fields K„{a, b) = Q{^jA„{a, b)). It is shown how the existence of a QRC for any a, b can be used to determine lower bounds on the class number of K„{...
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Let C ′ = C ∪ {∞} be the extended complex plane and M = 〈 x, y : x = y = 1 〉 , where x(z) = −1 3z and y(z) = −1 3(z+1) are the linear fractional transformations from C ′ → C ′ . Let m be a squarefree positive integer. Then Q∗( √ n) = { √ n c : a, c 6= 0, b = a 2−n c ∈ Z and (a, b, c) = 1} where n = km, is a proper subset of Q(√m) for all k ∈ N . For non-square n = 3 ri=1 pi i , it was proved in...
متن کاملReal Quadratic Number Fields
a4 + 1 a5 + .. . will see that a less wasteful notation, say [ a0 , a1 , a2 , . . . ] , is needed to represent it. Anyone attempting to compute the truncations [ a0 , a1 , . . . , ah ] = ph/qh will be delighted to notice that the definition [ a0 , a1 , . . . , ah ] = a0 + 1/[ a1 , . . . , ah ] immediately implies by induction on h that there is a correspondence ( a0 1 1 0 ) ( a1 1 1 0 ) · · · (...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1983
ISSN: 0386-2194
DOI: 10.3792/pjaa.59.390