# Concentration function of additive functions on shifted twin primes

Acta Arithmetica (1998)

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

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topSimon 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

top- [1] E. Bombieri, Le grand crible dans la théorie analytique des nombres, Astérisque 18 (1974).
- [2] P. D. T. A. Elliott, Probabilistic Number Theory, Vol. I, Springer, New York, 1979. Zbl0431.10029
- [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] P. D. T. A. Elliott, The concentration function of additive functions on shifted primes, Acta Math. 173 (1994), 1-35. Zbl0824.11057
- [5] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
- [6] H. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971. Zbl0216.03501
- [7] I. Z. Ruzsa, On the concentration of additive functions, Acta Math. Acad. Sci. Hungar. 36 (1980), 215-232. Zbl0471.10034
- [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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