ArticleOriginal scientific text

Title

A conditional result on Goldbach numbers in short intervals

Authors 1

Affiliations

  1. Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy

Bibliography

  1. H. Davenport, Multiplicative Number Theory, 2nd ed., Springer, 1980.
  2. J. B. Friedlander and D. A. Goldston, Some singular series averages and the distribution of Goldbach numbers in short intervals, Illinois J. Math. 39 (1995), 158-180.
  3. D. A. Goldston, Linnik's theorem on Goldbach numbers in short intervals, Glasgow Math. J. 32 (1990), 285-297.
  4. D. A. Goldston and H. L. Montgomery, Pair correlation of zeros and primes in short intervals, in: Analytic Number Theory and Dioph. Probl., A. C. Adolphson et al. (eds.), Birkhäuser, 1987, 183-203.
  5. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, 1990.
  6. D. R. Heath-Brown, Gaps between primes, and the pair correlation of zeros of the zeta-function, Acta Arith. 41 (1982), 85-99.
  7. L. K. Hua, Introduction to Number Theory, Springer, 1982.
  8. I. Kátai, A remark on a paper of Yu. V. Linnik, Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 17 (1967), 99-100 (in Hungarian).
  9. A. Languasco and A. Perelli, On Linnik's theorem on Goldbach numbers in short intervals and related problems, Ann. Inst. Fourier (Grenoble) 44 (1994), 307-322.
  10. A. Languasco and A. Perelli, A pair correlation hypothesis and the exceptional set in Goldbach's problem, Mathematika 43 (1996), 349-361.
  11. Yu. V. Linnik, Some conditional theorems concerning the binary Goldbach problem, Izv. Akad. Nauk SSSR Ser. Mat. 16 (1952), 503-520 (in Russian).
  12. H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, 1971.
  13. H. L. Montgomery, The pair correlation of zeros of the zeta function, in: Proc. Sympos. Pure Math. 24, Amer. Math. Soc., 1973, 181-193.
  14. H. L. Montgomery and R. C. Vaughan, The exceptional set in Goldbach's problem, Acta Arith. 27 (1975), 353-370.
  15. E. C. Titchmarsh, The Theory of Riemann Zeta-Function, 2nd ed., Oxford Univ. Press, 1986.
Pages:
93-103
Main language of publication
English
Received
1996-04-30
Accepted
1997-09-08
Published
1998
Exact and natural sciences