A singular series average and Goldbach numbers in short intervals

A. Languasco

Acta Arithmetica (1998)

  • Volume: 83, Issue: 2, page 171-179
  • ISSN: 0065-1036

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A. Languasco. "A singular series average and Goldbach numbers in short intervals." Acta Arithmetica 83.2 (1998): 171-179. <http://eudml.org/doc/207113>.

@article{A1998,
author = {A. Languasco},
journal = {Acta Arithmetica},
keywords = {short intervals; Riemann hypothesis; Riemann zeta function; pair correlation function; pair correlation hypothesis; Goldbach numbers in short intervals; asymptotic formula; Hardy-Littlewood singular series; binary Goldbach problem},
language = {eng},
number = {2},
pages = {171-179},
title = {A singular series average and Goldbach numbers in short intervals},
url = {http://eudml.org/doc/207113},
volume = {83},
year = {1998},
}

TY - JOUR
AU - A. Languasco
TI - A singular series average and Goldbach numbers in short intervals
JO - Acta Arithmetica
PY - 1998
VL - 83
IS - 2
SP - 171
EP - 179
LA - eng
KW - short intervals; Riemann hypothesis; Riemann zeta function; pair correlation function; pair correlation hypothesis; Goldbach numbers in short intervals; asymptotic formula; Hardy-Littlewood singular series; binary Goldbach problem
UR - http://eudml.org/doc/207113
ER -

References

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  1. [1] R. Baker, G. Harman and J. Pintz, The exceptional set for Goldbach's problem in short intervals, in: Proc. of Sieve Methods, Exponential Sums and Their Application in Number Theory, G. R. H. Greaves et al. (eds.), Cambridge Univ. Press, 1996, 1-54. Zbl0929.11042
  2. [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. Zbl0814.11048
  3. [3] D. A. Goldston, Linnik's theorem on Goldbach numbers in short intervals, Glasgow Math. J. 32 (1990), 285-297. Zbl0719.11065
  4. [4] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, 1974. 
  5. [5] I. Kátai, A remark on a paper of Yu. V. Linnik, Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 17 (1967), 99-100 (in Hungarian). 
  6. [6] A. Languasco, A conditional result on Goldbach numbers in short intervals, Acta Arith., this volume, 93-103. 
  7. [7] H. L. Montgomery and R. C. Vaughan, The exceptional set in Goldbach's problem, Acta Arith. 27 (1975), 353-370. Zbl0301.10043
  8. [8] K. Ramachandra, Two remarks in prime number theory, Bull. Soc. Math. France 105 (1977), 433-437. Zbl0381.10031
  9. [9] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Inst. E. Cartan 13, 1990. 
  10. [10] A. Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Deutscher Verlag Wiss., 1963. Zbl0146.06003

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