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Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients

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Inoue Y., Ota K.

Acta Arithmetica

2015

tom 169

nr 2

101-114

We consider the indices of subfields of cyclotomic ℤₚ-extensions of number fields. For the nth layer Kₙ of the cyclotomic ℤₚ-extension of ℚ, we find that the prime factors of the index of Kₙ/ℚ are those primes less than the extension degree pⁿ which split completely in Kₙ. Namely, the prime factor q satisfies $q^{p-1} ≡ 1 (mod p^{n+1})$, and this leads us to consider higher degree Fermat quotients. Indices of subfields of cyclotomic ℤₚ-extensions of a number field which is cyclic over ℚ with extension degree a prime different from p are also considered.

Ograniczanie wyników

1 Acta Arithmetica

1 Inoue Y.

1 Ota K.

1 2015

Wyniki wyszukiwania

Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients