On the Size of the Rst Factor of the Class Number of a Cyclotomic Eld
نویسنده
چکیده
We show that Kummer's conjectured asymptotic estimate for the size of the rst factor of the class number of a cyclotomic eld is untrue under the assumption of two well-known and widely believed conjectures of analytic number theory.
منابع مشابه
Unit 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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تاریخ انتشار 1990