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A note on the exceptional set for Goldbach's problem in short intervals

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Abstract

Assume the Generalized Riemann Hypothesis and suppose thatHlog−6 x→t8. Then we prove that all even integers in any interval of the form (x, x, +H) butO(H1/2log3x) exceptions are a sum of two primes.

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Authors and Affiliations

  1. Institute of Mathematics, A. Mickiewicz University, Poznań, Poland

    J. Kaczorowski

  2. Dipartimento di Matematica, Università di Genova, Via L. B. Alberti 4, I-16132, Genova, Italia

    A. Perelli

  3. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1364, Budapest, Hungary

    J. Pintz

Authors
  1. J. Kaczorowski
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  2. A. Perelli
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  3. J. Pintz
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Additional information

Partially supported by Consiglio Nazionale delle Ricerche, Visiting Professor Program.

Partially supported by Hungarian National Foundation for Scientific Research, Grant n. 1901.

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Kaczorowski, J., Perelli, A. & Pintz, J. A note on the exceptional set for Goldbach's problem in short intervals. Monatshefte für Mathematik 116, 275–282 (1993). https://doi.org/10.1007/BF01301533

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  • DOI: https://doi.org/10.1007/BF01301533

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