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1995 | 72 | 2 | 131-167
Tytuł artykułu

Short intervals almost all containing primes

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
72
Numer
2
Strony
131-167
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-06-17
poprawiono
1994-12-12
Twórcy
autor
  • Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
Bibliografia
  • [1] R. C. Baker and G. Harman, The difference between consecutive primes, preprint.
  • [2] A. Buchstab, Asymptotic estimates of a general number-theoretic function, Mat. Sb. (N.S.) (2) 44 (1937), 1239-1246 (in Russian with a German summary).
  • [3] H. Davenport, Multiplicative Number Theory, Springer, 1980.
  • [4] J.-M. Deshouillers and H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70 (1982), 219-288.
  • [5] J.-M. Deshouillers and H. Iwaniec, Power mean values of the Riemann zeta-function, Mathematika 29 (1982), 202-212.
  • [6] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Clarendon Press, Oxford, 1954.
  • [7] G. Harman, Almost-primes in short intervals, Math. Ann. 258 (1981), 107-112.
  • [8] G. Harman, Primes in short intervals, Math. Z. 180 (1982), 335-348.
  • [9] G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2) 27 (1983), 9-18.
  • [10] G. Harman, On the distribution of αp modulo one II, preprint.
  • [11] D. R. Heath-Brown, Gaps between primes and the pair correlation of zeros of the zeta-function, Acta Arith. 41 (1982), 85-99.
  • [12] D. R. Heath-Brown, Finding primes by sieve methods, Proc. 1982 ICM, Warsaw, 1983, PWN, Vol. 1, Warszawa, 1984, 487-492.
  • [13] D. R. Heath-Brown and H. Iwaniec, On the difference between consecutive primes, Invent. Math. 55 (1979), 49-69.
  • [14] M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170.
  • [15] H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202.
  • [16] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320.
  • [17] H. Iwaniec and M. Jutila, Primes in short intervals, Ark. Mat. 17 (1979), 167-176.
  • [18] H. Iwaniec and J. Pintz, Primes in short intervals, Monatsh. Math. 98 (1984), 115-143.
  • [19] C. Jia, On the Goldbach numbers in the short interval, Science in China, to appear.
  • [20] C. Jia, On the difference between consecutive primes, Science in China,, to appear.
  • [21] H. Li, Primes in short intervals, unpublished manuscript.
  • [22] H. Li, Primes in short intervals, preprint.
  • [23] S. Lou and Q. Yao, A Chebychev's type of prime number theorem in a short interval - II, Hardy-Ramanujan J. 15 (1992), 1-33.
  • [24] H. Mikawa, Almost-primes in arithmetic progressions and short intervals, Tsukuba J. Math. (2) 13 (1989), 387-401.
  • [25] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, 1971.
  • [26] H. L. Montgomery and R. C. Vaughan, Hilbert's inequality, J. London Math. Soc. (2) 8 (1974), 73-82.
  • [27] H. L. Montgomery and R. C. Vaughan, The exceptional set in Goldbach's problem, Acta Arith. 27 (1975), 353-370.
  • [28] Y. Motohashi, A note on almost-primes in short intervals, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), 225-226.
  • [29] C. J. Mozzochi, On the difference between consecutive primes, J. Number Theory 24 (1986), 181-187.
  • [30] A. Perelli and J. Pintz, On the exceptional set for Goldbach's Problem in short intervals, J. London Math. Soc. (2) 47 (1993), 41-49.
  • [31] A. Selberg, On the normal density of primes in short intervals, and the difference between consecutive primes, Arch. Math. Naturvid. 47 (1943), 87-105.
  • [32] P. Shiu, A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math. 313 (1980), 161-170.
  • [33] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Clarendon Press, Oxford, 1986.
  • [34] N. Watt, Kloosterman sums and a mean value for Dirichlet polynomials, J. Number Theory, to appear.
  • [35] D. Wolke, Fast-Primzahlen in kurzen Intervallen, Math. Ann. 224 (1979), 233-242
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav72i2p131bwm
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