منابع مشابه
Class Numbers of Real Quadratic Number Fields by Ezra Brown
This article is a study of congruence conditions, modulo powers of two, on class number of real quadratic number fields Q(vu), for which d has at most thtee distinct prime divisors. Techniques used are those associated with Gaussian composition of binary quadratic forms. 1. Let hid) denote the class number of the quadratic field Qi\ß) and let h id) denote the number of classes of primitive bina...
متن کاملComputation of class numbers of quadratic number fields
We explain how one can dispense with the numerical computation of approximations to the transcendental integral functions involved when computing class numbers of quadratic number fields. We therefore end up with a simpler and faster method for computing class numbers of quadratic number fields. We also explain how to end up with a simpler and faster method for computing relative class numbers ...
متن کاملOn a Class Number Formula for Real Quadratic Number Fields
For an even Dirichlet character , we obtain a formula for L(1;) in terms of a sum of Dirichlet L-series evaluated at s = 2 and s = 3 and a rapidly convergent numerical series involving the central binomial coeecients. We then derive a class number formula for real quadratic number elds by taking L(s;) to be the quadratic L-series associated with these elds.
متن کاملComputations of class numbers of real quadratic fields
In this paper an unconditional probabilistic algorithm to compute the class number of a real quadratic field Q( √ d) is presented, which computes the class number in expected time O(d1/5+ ). The algorithm is a random version of Shanks’ algorithm. One of the main steps in algorithms to compute the class number is the approximation of L(1, χ). Previous algorithms with the above running time O(d1/...
متن کاملIndivisibility of Class Numbers of Real Quadratic Fields
Although the literature on class numbers of quadratic fields is quite extensive, very little is known. In this paper we consider class numbers of real quadratic fields, and as an immediate consequence we obtain an estimate for the number of vanishing Iwasawa λ invariants. Throughout D will denote the fundamental discriminant of the quadratic number fieldQ( √ D), h(D) its class number, and χD :=...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1974-0364172-9