Class numbers of real quadratic function fields
نویسندگان
چکیده
منابع مشابه
Computations 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 :=...
متن کاملANote on the Divisibilityof Class Numbers of Real Quadratic Fields
Suppose g > 2 is an odd integer. For real number X > 2, define SgðXÞ the number of squarefree integers d4X with the class number of the real quadratic field Qð ffiffiffi d p Þ being divisible by g. By constructing the discriminants based on the work of Yamamoto, we prove that a lower bound SgðXÞ4X 1=g e holds for any fixed e > 0, which improves a result of Ram Murty. # 2002 Elsevier Science (USA)
متن کاملClass 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 کاملClass numbers of ray class fields of imaginary quadratic fields
Let K be an imaginary quadratic field with class number one and let p ⊂ OK be a degree one prime ideal of norm p not dividing 6dK . In this paper we generalize an algorithm of Schoof to compute the class numbers of ray class fields Kp heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura’s reciprocity law. We have...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1997
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-81-1-45-55