Computation of real quadratic fields with class number one
نویسندگان
چکیده
منابع مشابه
Computation of Real Quadratic Fields with Class Number One
A rapid method for determining whether the real quadratic field Sí = S(\/D) has class number one is described. The method makes use of the infrastructure idea of Shanks to determine the regulator of .W and then uses the Generalized Riemann Hypothesis to rapidly estimate L(l, x) to the accuracy needed for determining whether or not the class number of 3£ is one. The results of running this algor...
متن کاملComputation of p-units in ray class fields of real quadratic number fields
Abstract. Let K be a real quadratic field, let p be a prime number which is inert in K and let Kp be the completion of K at p. As part of a Ph.D. thesis, we constructed a certain p-adic invariant u ∈ K× p , and conjectured that u is, in fact, a p-unit in a suitable narrow ray class field of K. In this paper we give numerical evidence in support of that conjecture. Our method of computation is s...
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 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 ) · · · (...
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: Mathematics of Computation
سال: 1988
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1988-0958644-7