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Galois module structure of rings of integers

Martin J. Taylor (1980)

Annales de l'institut Fourier

Let E / F be a Galois extension of number fields with Γ = Gal ( E / F ) and with property that the divisors of ( E : F ) are non-ramified in E / Q . We denote the ring of integers of E by 𝒪 E and we study 𝒪 E as a Z Γ -module. In particular we show that the fourth power of the (locally free) class of 𝒪 E is the trivial class. To obtain this result we use Fröhlich’s description of class groups of modules and his representative for the class of E , together with new determinantal congruences for cyclic group rings and corresponding congruences...

Gaps between primes in Beatty sequences

Roger C. Baker, Liangyi Zhao (2016)

Acta Arithmetica

We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).

Goldbach numbers in sparse sequences

Jörg Brüdern, Alberto Perelli (1998)

Annales de l'institut Fourier

We show that for almost all n N , the inequality | p 1 + p 2 - exp ( ( log n ) γ ) | < 1 has solutions with odd prime numbers p 1 and p 2 , provided 1 < γ < 3 2 . Moreover, we give a rather sharp bound for the exceptional set.This result provides almost-all results for Goldbach numbers in sequences rather thinner than the values taken by any polynomial.

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