ArticleOriginal scientific text

Title

Problems and results on αp - βq

Authors 1, 1, 1

Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Bombay 400 005, India

Keywords

primes, inequalities, Harman's result, Selberg's sieve, Brun's sieve

Bibliography

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  2. H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London, 1974.
  3. G. Harman, Primes in short intervals, Math. Z. 180 (1982), 335-348.
  4. G. Harman, Almost primes in short intervals, Math. Ann. 258 (1981), 107-112.
  5. A. Ivić, The Riemann Zeta-function, Wiley-Interscience, New York, 1985.
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  7. 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.
  8. H. L. Montgomery and R. C. Vaughan, The exceptional set of Goldbach's problem, Acta Arith. 27 (1975), 353-370.
  9. Y. Motohashi, A note on almost primes in short intervals, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), 225-226.
  10. K. Ramachandra, Two remarks in prime number theory, Bull. Soc. Math. France 105 (1977), 433-437.
  11. K. Ramachandra, Viggo Brun (13-10-1885 to 15-8-1978), Math. Student 49 (1981), 97-95.
  12. K. Ramachandra, A. Sankaranarayanan and K. Srinivas, Ramanujan's lattice point problem, prime number theory and other remarks, Hardy-Ramanujan J. 19 (1996), 2-56.
  13. H.-E. Richert, Sieve Methods, Lecture Notes 55, Tata Institute of Fundamental Research, Bombay, 1976.
  14. A. Selberg, On the normal density of primes in small intervals, and the difference between consecutive primes, Arch. Math. Naturvid. 47 (1943), 87-105.
  15. S. Srinivasan, A note on |αp -q|, Acta Arith. 41 (1982), 15-18.
  16. D. Wolke, Fast-Primzahlen in kurzen Intervallen, Math. Ann. 244 (1979), 233-242.
Pages:
119-131
Main language of publication
English
Received
1995-05-29
Published
1996
Exact and natural sciences