1. On the Iwasawa invariants of prime cyclotomic fields.
- Author
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Kim, Sey Y.
- Subjects
- *
PRIME numbers , *CYCLOTOMIC fields , *INTEGERS , *LOGICAL prediction - Abstract
Let p > 3 be a prime number, ζ be a primitive p-th root of unity. Suppose that the Kummer-Vandiver conjecture holds for p , i.e., that p does not divide the class number of Q (ζ + ζ - 1) . Let λ and ν be the Iwasawa invariants of Q (ζ) and put λ = : ∑ i ∈ I λ i and ν = : ∑ i ∈ I ν i in the usual way, where I is the set of odd integers in { 3 , ... , p - 2 } . We prove for each i ∈ I that λ i ≤ 1 , so that the p-primary part of class group of each Q (exp (2 π - 1 / p n)) is determined by the set { (i , ν i) : i ∈ I } . [ABSTRACT FROM AUTHOR]
- Published
- 2023
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