Problems and results on αp - βq

• Autorzy: K. Ramachandra , A. Sankaranarayanan , K. Srinivas
• Języki publikacji: EN

Słowa kluczowe

EN

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

Kategorie tematyczne

• 11N05: Distribution of primes
• 11Nxx: Multiplicative number theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 75
• Numer: 2
• Strony: 119-131

Daty

wydano

1996

otrzymano

1995-05-29

Twórcy

autor

K. Ramachandra

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

autor

A. Sankaranarayanan

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

autor

K. Srinivas

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

Bibliografia

• [1] E. Bombieri and H. Davenport, Small differences between prime numbers, Proc. Roy. Soc. London Ser. A 293 (1966), 1-18.
• [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.
• [6] L. F. Kondakova and N. I. Klimov, Certain additive problems, Volzh. Mat. Sb. 7 (1969), 41-44 (in Russian).
• [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.