Concentration function of additive functions on shifted twin primes

Simon Wong

Acta Arithmetica (1998)

  • Volume: 84, Issue: 3, page 193-224
  • ISSN: 0065-1036

Abstract

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0. Introduction. The content of this paper is part of the author's Ph.D. thesis. The two new theorems in this paper provide upper bounds on the concentration function of additive functions evaluated on shifted γ-twin prime, where γ is any positive even integers. Both results are generalizations of theorems due to I. Z. Ruzsa, N. M. Timofeev, and P. D. T. A. Elliott.

How to cite

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Simon Wong. "Concentration function of additive functions on shifted twin primes." Acta Arithmetica 84.3 (1998): 193-224. <http://eudml.org/doc/269868>.

@article{SimonWong1998,
abstract = {0. Introduction. The content of this paper is part of the author's Ph.D. thesis. The two new theorems in this paper provide upper bounds on the concentration function of additive functions evaluated on shifted γ-twin prime, where γ is any positive even integers. Both results are generalizations of theorems due to I. Z. Ruzsa, N. M. Timofeev, and P. D. T. A. Elliott.},
author = {Simon Wong},
journal = {Acta Arithmetica},
keywords = {shifted twin primes; Bombieri-type theorems for multiplicative functions; Selberg's sieve method; Bombieri-Vinogradov theorem; asymptotic estimates; additive function},
language = {eng},
number = {3},
pages = {193-224},
title = {Concentration function of additive functions on shifted twin primes},
url = {http://eudml.org/doc/269868},
volume = {84},
year = {1998},
}

TY - JOUR
AU - Simon Wong
TI - Concentration function of additive functions on shifted twin primes
JO - Acta Arithmetica
PY - 1998
VL - 84
IS - 3
SP - 193
EP - 224
AB - 0. Introduction. The content of this paper is part of the author's Ph.D. thesis. The two new theorems in this paper provide upper bounds on the concentration function of additive functions evaluated on shifted γ-twin prime, where γ is any positive even integers. Both results are generalizations of theorems due to I. Z. Ruzsa, N. M. Timofeev, and P. D. T. A. Elliott.
LA - eng
KW - shifted twin primes; Bombieri-type theorems for multiplicative functions; Selberg's sieve method; Bombieri-Vinogradov theorem; asymptotic estimates; additive function
UR - http://eudml.org/doc/269868
ER -

References

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  1. [1] E. Bombieri, Le grand crible dans la théorie analytique des nombres, Astérisque 18 (1974). 
  2. [2] P. D. T. A. Elliott, Probabilistic Number Theory, Vol. I, Springer, New York, 1979. Zbl0431.10029
  3. [3] P. D. T. A. Elliott, Multiplicative functions on arithmetic progressions. VI. More middle moduli, J. Number Theory 44 (1993), 178-208. Zbl0780.11042
  4. [4] P. D. T. A. Elliott, The concentration function of additive functions on shifted primes, Acta Math. 173 (1994), 1-35. Zbl0824.11057
  5. [5] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
  6. [6] H. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971. Zbl0216.03501
  7. [7] I. Z. Ruzsa, On the concentration of additive functions, Acta Math. Acad. Sci. Hungar. 36 (1980), 215-232. Zbl0471.10034
  8. [8] N. M. Timofeev, The Erdős-Kubilius conjecture concerning the value distribution of additive functions on the sequence of shifted primes, Acta Arith. 58 (1991), 113-131 (in Russian). 

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