A Generalized Problem Associated to the Kummer–Vandiver Conjecture

Autor: Hiroki Sumida-Takahashi
Rok vydání: 2022
Předmět:
Zdroj: Arnold Mathematical Journal.
ISSN: 2199-6806
2199-6792
DOI: 10.1007/s40598-022-00220-3
Popis: In order to discuss the validity of the Kummer-Vandiver conjecture, we consider a generalized problem associated to the conjecture. Let p be an odd prime number and ζp a primitive p-th root of unity. Using new programs, we compute the Iwasawa invariants of Q(√d, ζp) in the range |d| < 200 and 200 < p < 1,000,000. From our data, the actual numbers of exceptional cases seem to be near the expected numbers for p < 1,000,000. Moreover, we find a few rare exceptional cases for |d| < 10 and p > 1,000,000. We give two partial reasons why it is difficult to find exceptional cases for d = 1 including counter-examples to the Kummer-Vandiver conjecture.
Databáze: OpenAIRE
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