The Class Number of the Cyclotomic Field
نویسندگان
چکیده
منابع مشابه
The 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 کاملUnit Fractions and the Class Number of a Cyclotomic Field
We further examine Kummer's incorrect conjectured asymptotic estimate for the size of the rst factor of the class number of a cyclotomic eld, h 1 (p). Whereas Kummer had conjectured that h 1 (p) G(p) := 2p(p=4 2) p?1 4 we show, under certain plausible assumptions, that there exist constants a ; b such that h 1 (p) G(p) for a x= log b x primes p x whenever log is rational. On the other hand, the...
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We study the parity of the class number of the pth cyclotomic field for p prime. By analytic methods we derive a parity criterion in terms of polynomials over the field of 2 elements. The conjecture that the class number is odd for p a prime of the form 2q +1, with q prime, is proved in special cases, and a heuristic argument is given in favor of the conjecture. An implementation of the criteri...
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The values of the first factor Hx(m) of the class number of the with cyclotomic field are tabulated for 120 composite rre's larger than 100. A conjecture concerning a divisibility property of Hx{m) is stated.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1949
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.35.9.529