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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.

Incomplete character sums and a special class of permutations

S. D. Cohen, H. Niederreiter, I. E. Shparlinski, M. Zieve (2001)

Journal de théorie des nombres de Bordeaux

We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an -orthomorphism. Examples of -orthomorphisms are given.

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