Annihilators for the class group of a cyclic field of prime power degree
C. Greither, R. Kučera (2004)
Acta Arithmetica
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C. Greither, R. Kučera (2004)
Acta Arithmetica
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Haiyan Zhou (2009)
Acta Arithmetica
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D. Martinalis, L. Schneps (1993)
Manuscripta mathematica
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Franz Lemmermeyer (2005)
Journal de Théorie des Nombres de Bordeaux
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In this note we give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger’s theorem.
John Myron Masley (1978)
Compositio Mathematica
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Xia Wu (2008)
Acta Arithmetica
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C. Greither (1989)
Manuscripta mathematica
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Yoko Inoue, Kaori Ota (2015)
Acta Arithmetica
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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 , 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...
John Myron Masley (1976)
Compositio Mathematica
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Richard Massy (2009)
Acta Arithmetica
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R. Gold, H. Kisilevsky (1988)
Manuscripta mathematica
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Claus Scheiderer (1991)
Manuscripta mathematica
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Hiroo Miki (1981)
Journal für die reine und angewandte Mathematik
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