Humio Ichimura
Abstract
Abstract For an odd prime number p and an integer n ≥ 0, let h n be the class number of the p n+1st cyclotomic field Q($$ \zeta _{p^{n + 1} } $$). It is known that when p = 3 or 5, h n is odd for all n ≥ 0. We prove that the same holds also when p = 7.
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Abstract For an odd prime number p and an integer n ≥ 0, let h n be the class number of the p n+1st cyclotomic field Q($$ \zeta _{p^{n + 1} } $$). It is known that when p = 3 or 5, h n is odd for all n ≥ 0. We prove that the same holds also when p = 7.
Key concepts: Mathematics, Cyclotomic field, Class number, Parity (physics), Class (philosophy), Combinatorics, Algebraic number field, Integer (computer science)