Note on Bernoulli numbers associated to some Dirichlet character of prime conductor

“…This is nothing but h − p when n is a power of 2. In addition to the case n = 2 e with 0 ≤ e ≤ 4, it is known that for n = 3 or 5, h − N is odd when 2 is a primitive root modulo ( [11,Remark 2], [12,Corollary 1]). In this paper, we generalize these results on the parity of h − N as follows, with the help of computer.…”

Section: Introductionmentioning

confidence: 99%

Note on class number parity of an abelian field of prime conductor

Fujima

Ichimura

2018

Mathematical journal of Ibaraki University

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Triviality of Iwasawa module associated to some abelian fields of prime conductors

Ichimura

2017

Abh. Math. Semin. Univ. Hambg.

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Biographical Sketch of Professor Humio Ichimura

2022

Mathematical journal of Ibaraki University

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After that, he entered graduate school of the University of Tokyo; master course (1979) and then doctor course (1981). He got his master degree in 1981. His master thesis dealt with a divisibility problem of class numbers of certain number fields. He got his doctoral degree under the supervision of Professor Y. Ihara (1987). The title of his treatise was "On several power series which appear in the theory of cyclotomic fields".In September, 1988, he was hired as an associate professor of Yokohama City University. This year is almost the last of Showa period (the last day is January, 7, 1989). In the same month of the year, Professor K. Iwasawa started a seminar on number theory (Komaba seminar) at Komaba Campus of the University of Tokyo, after coming back to Japan in 1987. Humio Ichimura was a member of the seminar from the beginning, and there, he studied classical Iwasawa theory on cyclotomic fields. He moved to the Faculty of Sciences, Ibaraki University as a professor in April, 2005, and retired in March, 2022. Humio Ichimura's research area is algebraic number theory. He addressed various classical problems on • class number and class group of a number field • ring of integers of a number field such as: 1. divisibility of class numbers of number fields, 2. indivisibility of class numbers of number fields, 3. class numbers of algebraic function fields, 4. Iwasawa invariants and modules associated to abelian fields, 5. Gauss sums in local abelian fields, 6. non p-part of the class numbers in a cyclotomic Z p -extension, 7. class numbers in cyclotomic fields of prime conductors, 8. power integral basis of a cyclic extension of a number field, 9. normal integral basis of a cyclic extension of a number field, 10. Hilbert-Speiser number fields.

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Note on Bernoulli numbers associated to some Dirichlet character of prime conductor

Cited by 3 publications

References 10 publications

Note on class number parity of an abelian field of prime conductor

Note on class number parity of an abelian field of prime conductor

Triviality of Iwasawa module associated to some abelian fields of prime conductors

Biographical Sketch of Professor Humio Ichimura

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