Displaying similar documents to “Cyclotomy in G . D . ( p α q β r γ ) ”

On the power-series expansion of a rational function

D. V. Lee (1992)

Acta Arithmetica

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Introduction. The problem of determining the formula for P S ( n ) , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, h s ₁ , . . . , h s k , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of x ⁿ i n [(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part...

The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems

Cornelius Greither, Radiu Kučera (2002)

Annales de l’institut Fourier

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The so-called Lifted Root Number Conjecture is a strengthening of Chinburg’s Ω ( 3 ) - conjecture for Galois extensions K / F of number fields. It is certainly more difficult than the Ω ( 3 ) -localization. Following the lead of Ritter and Weiss, we prove the Lifted Root Number Conjecture for the case that F = ℚ and the degree of K / F is an odd prime, with another small restriction on ramification. The very explicit calculations with cyclotomic units use trees and some classical combinatorics for bookkeeping....