

А.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications
May 22, 2017 12:50–13:20, Moscow, Steklov Mathematical Institute






The Ternary Goldbach Problem with a prime and two isolated primes (joint paper with M.T. Rassias)
H. Maier^{} ^{} University of Ulm

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Abstract:
The concept of an isolated prime is closely related to the problem of large gaps between consecutive primes.
This problem has mainly been studied by the Erdös  Rankin method and its extensions.
Recently a significant improvement of the result has been achieved by Ford, Green, Konyagin, Maynard and Tao.
The authors of the present paper combine the results and methods of these five authors with the circle method,
which first has been applied to the ternary Goldbach problem by I.M. Vinogradov. His result has been extended
to various special sets of primes, e.g. primes in arithmetic progressions.
By considering primes in residueclasses, they have constructed by the improved ErdösRankin method,
the authors obtain the following
Theorem. Under assumption of the Generalized Riemann Hypothesis each sufficiently
large odd integer can be expressed as the sum of a prime and two isolated primes.
Language: English

