Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE p-PART OF DIVISOR CLASS NUMBERS FOR CYCLOTOMIC FUNCTION FIELDS

  • Daisuke Shiomi (Department of Science Faculty of Science Yamagata University)
  • Received : 2022.09.09
  • Accepted : 2023.02.07
  • Published : 2023.07.31
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Abstract

In this paper, we construct explicitly an infinite family of primes P with h±P ≡ 0 (mod qdeg P), where h±P are the plus and minus parts of the divisor class number of the P-th cyclotomic function field over 𝔽q(T). By using this result and Dirichlet's theorem, we give a condition of A, M ∈ 𝔽q[T] such that there are infinitely many primes P satisfying with h±P ≡ 0 (mod pe) and P ≡ A (mod M).

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Acknowledgement

The author would like to thank the referee for many helpful suggestions.

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