A conditional result on Goldbach numbers in short intervals

• Autorzy: A. Languasco
• Języki publikacji: EN

Kategorie tematyczne

• 11P32: Goldbach-type theorems; other additive questions involving primes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 83
• Numer: 2
• Strony: 93-103

Daty

wydano

1998

otrzymano

1996-04-30

poprawiono

1997-09-08

Twórcy

autor

A. Languasco

• Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy

Bibliografia

• [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.