A Generalised Kummer’s Conjecture
نویسنده
چکیده
Let Q(ζm) be the mth cyclotomic field, where ζm is a primitive mth root of unity for an integer m ≥ 1. Let hm denote the class number of Q(ζm) and hm be the class number of its maximal real subfield Q(ζm + ζ −1 m ). Kummer proved that the relative class number hm = hm/h + m is an integer, and in 1851 he claimed ([7], pg. 473) that the rule for the asymptotic growth of hp as the prime p → ∞ is given by the formula p(p+3)/4 2(p−3)/2π(p−1)/2 =: G(p). (1)
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