Displaying similar documents to “Goldbach numbers in sparse sequences”

On the almost Goldbach problem of Linnik

Jianya Liu, Ming-Chit Liu, Tianze Wang (1999)

Journal de théorie des nombres de Bordeaux

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Under the Generalized Riemann Hypothesis, it is proved that for any k ≥ 200 there is N k > 0 depending on k only such that every even integer ≥ N k is a sum of two odd primes and k powers of 2 .

On an estimate of Walfisz and Saltykov for an error term related to the Euler function

Y.-F. S. Pétermann (1998)

Journal de théorie des nombres de Bordeaux

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The technique developed by A. Walfisz in order to prove (in 1962) the estimate H ( x ) ≪ ( log x ) 2 / 3 ( log log x ) 4 / 3 for the error term H ( x ) = ∑ n ≤ x φ ( n ) n - 6 π 2 x related to the Euler function is extended. Moreover, the argument is simplified by exploiting works of A.I. Saltykov and of A.A. Karatsuba. It is noted in passing that the proof proposed by Saltykov in 1960 of H ( x ) ≪ ( log x ) 2 / 3 ( log log x ) 1 + ϵ is erroneous and once corrected “only” yields Walfisz’ result. The generalizations obtained can be applied to error terms related to various classical - and less classical -...