Lower Bounds for Relative Class Numbers of CM-Fields
نویسندگان
چکیده
منابع مشابه
EXPLICIT LOWER BOUNDS FOR RESIDUES AT s = 1 OF DEDEKIND ZETA FUNCTIONS AND RELATIVE CLASS NUMBERS OF CM-FIELDS
Let S be a given set of positive rational primes. Assume that the value of the Dedekind zeta function ζK of a number field K is less than or equal to zero at some real point β in the range 1 2 < β < 1. We give explicit lower bounds on the residue at s = 1 of this Dedekind zeta function which depend on β, the absolute value dK of the discriminant of K and the behavior in K of the rational primes...
متن کاملFast Computation of Relative Class Numbers of CM-Fields
It was well known that it is easy to compute relative class numbers of abelian CM-fields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, Springer-Verlag, 1982). Here, we provide a technique for computing the relative class number of any CM-field. 1. Statement of the results Proposition 1. Let n ≥ 1...
متن کاملComputation of Relative Class Numbers of Cm-fields
It was well known that it is easy to compute relative class numbers of abelian CM-fields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, Springer-Verlag, 1982). Here, we provide a technique for computing the relative class number of any CM-field. 1. Statement of the results Proposition 1. Let n ≥ 1...
متن کاملCM-fields with relative class number one
We will show that the normal CM-fields with relative class number one are of degrees ≤ 216. Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees ≤ 96, and the CM-fields with class number one are of degrees ≤ 104. By many authors all normal CM-fields of degrees ≤ 96 with class number one are known except for the possib...
متن کاملBrauer-Siegel like results for relative class numbers of CM-fields
We prove Brauer-Siegel like results about the asymptotic behavior of relative class numbers of CM-fields. 01991 Mathematics Subject Classification. Primary 11R42, 11M. Secondary 11R29.
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: Proceedings of the American Mathematical Society
سال: 1994
ISSN: 0002-9939
DOI: 10.2307/2159878