"Almost every" algebraic number-field has a large class-number
نویسندگان
چکیده
منابع مشابه
Almost Every Number Has a Continuum of β-Expansions
where b·c denotes the integral part of a number and {·} stands for its fractional part. If x belongs to [1, 1/(β − 1)), then we put ` = min {k ≥ 1 : x− β−1 − · · · − β−k ∈ (0, 1)} and apply the greedy algorithm to x − β−1 − · · · − β to obtain the digits ε`+1, ε`+2, etc. Finally, if x = 1/(β − 1), then εn = 1 for all n. The question then arises: Are there any other β-expansions of a given x bes...
متن کاملEvery Odd Perfect Number Has a Prime Factor Which Exceeds
It is proved here that every odd perfect number is divisible by a prime greater than 106.
متن کاملOn the Computation of the Class Number of an Algebraic Number Field
It is shown how the analytic class number formula can be used to produce an algorithm which efficiently computes the class number h of an algebraic number field F. The method assumes the truth of the Generalized Riemann Hypothesis in order to estimate the residue of the Dedekind zeta function of F at s = 1 sufficiently well that h can be determined unambiguously. Given the regulator R of F and ...
متن کاملThe Class Number of the Cyclotomic Field.
1. Let g denote any odd prime and h = h(g) the class number of the cyclotomic field R(r), where r is the primitive gth root of unity, R the rational numbers. It is known that we can write: h = h1h2, where hi and h2 (both integers) are the so-called first and second factors of the class number; in fact h2 is the class number of the real field of degree 2 under R(r), namely the field R(D + D-). K...
متن کاملReal Quadratic Orders with Large Class Number
Acknowledgements I am undoubtedly indebted to my two supervisors, Alf van der Poorten and Hugh Williams. Most students would feel lucky to have one good supervisor whereas I had the privilege of having two excellent mathematicians to guide me. Their help, wisdom and infinite patience has been invaluable, and I am very grateful for it. The Mathematics Department at Macquarie University has provi...
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: 1974
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-25-4-411-413