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

• Autorzy: Yoko Inoue , Kaori Ota
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11R04: Algebraic numbers; rings of algebraic integers
• 11R99: None of the above, but in this section
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 169
• Numer: 2
• Strony: 101-114

Daty

wydano

2015

Twórcy

autor

Yoko Inoue

• Department of Mathematics, Tsuda College, 2-1-1 Tsuda-cho, Kodaira-shi, Tokyo 187-8577, Japan

autor

Kaori Ota

• Department of Mathematics, Tsuda College, 2-1-1 Tsuda-cho, Kodaira-shi, Tokyo 187-8577, Japan

Identyfikatory

DOI

10.4064/aa169-2-1