Problems and results on αp - βq

K. Ramachandra; A. Sankaranarayanan; K. Srinivas

Acta Arithmetica (1996)

  • Volume: 75, Issue: 2, page 119-131
  • ISSN: 0065-1036

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K. Ramachandra, A. Sankaranarayanan, and K. Srinivas. "Problems and results on αp - βq." Acta Arithmetica 75.2 (1996): 119-131. <http://eudml.org/doc/206866>.

@article{K1996,
author = {K. Ramachandra, A. Sankaranarayanan, K. Srinivas},
journal = {Acta Arithmetica},
keywords = {primes; inequalities; Harman's result; Selberg's sieve; Brun's sieve; Goldbach numbers; simultaneous inequalities},
language = {eng},
number = {2},
pages = {119-131},
title = {Problems and results on αp - βq},
url = {http://eudml.org/doc/206866},
volume = {75},
year = {1996},
}

TY - JOUR
AU - K. Ramachandra
AU - A. Sankaranarayanan
AU - K. Srinivas
TI - Problems and results on αp - βq
JO - Acta Arithmetica
PY - 1996
VL - 75
IS - 2
SP - 119
EP - 131
LA - eng
KW - primes; inequalities; Harman's result; Selberg's sieve; Brun's sieve; Goldbach numbers; simultaneous inequalities
UR - http://eudml.org/doc/206866
ER -

References

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  1. [1] E. Bombieri and H. Davenport, Small differences between prime numbers, Proc. Roy. Soc. London Ser. A 293 (1966), 1-18. Zbl0151.04201
  2. [2] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
  3. [3] G. Harman, Primes in short intervals, Math. Z. 180 (1982), 335-348. Zbl0482.10040
  4. [4] G. Harman, Almost primes in short intervals, Math. Ann. 258 (1981), 107-112. Zbl0474.10034
  5. [5] A. Ivić, The Riemann Zeta-function, Wiley-Interscience, New York, 1985. Zbl0556.10026
  6. [6] L. F. Kondakova and N. I. Klimov, Certain additive problems, Volzh. Mat. Sb. 7 (1969), 41-44 (in Russian). 
  7. [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. Zbl0780.11039
  8. [8] H. L. Montgomery and R. C. Vaughan, The exceptional set of Goldbach's problem, Acta Arith. 27 (1975), 353-370. Zbl0301.10043
  9. [9] Y. Motohashi, A note on almost primes in short intervals, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), 225-226. Zbl0445.10032
  10. [10] K. Ramachandra, Two remarks in prime number theory, Bull. Soc. Math. France 105 (1977), 433-437. Zbl0381.10031
  11. [11] K. Ramachandra, Viggo Brun (13-10-1885 to 15-8-1978), Math. Student 49 (1981), 97-95. 
  12. [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. Zbl0824.11061
  13. [13] H.-E. Richert, Sieve Methods, Lecture Notes 55, Tata Institute of Fundamental Research, Bombay, 1976. 
  14. [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. Zbl0063.06869
  15. [15] S. Srinivasan, A note on |αp -q|, Acta Arith. 41 (1982), 15-18. 
  16. [16] D. Wolke, Fast-Primzahlen in kurzen Intervallen, Math. Ann. 244 (1979), 233-242. Zbl0402.10042

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