ArticleOriginal scientific text
Title
Concentration function of additive functions on shifted twin primes
Authors 1
Affiliations
- Department of Mathematical Sciences, Station #18, Eastern New Mexico University, Portales, New Mexico 88130, U.S.A.
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.
Bibliography
- E. Bombieri, Le grand crible dans la théorie analytique des nombres, Astérisque 18 (1974).
- P. D. T. A. Elliott, Probabilistic Number Theory, Vol. I, Springer, New York, 1979.
- P. D. T. A. Elliott, Multiplicative functions on arithmetic progressions. VI. More middle moduli, J. Number Theory 44 (1993), 178-208.
- P. D. T. A. Elliott, The concentration function of additive functions on shifted primes, Acta Math. 173 (1994), 1-35.
- H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974.
- H. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971.
- I. Z. Ruzsa, On the concentration of additive functions, Acta Math. Acad. Sci. Hungar. 36 (1980), 215-232.
- 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).
Pages:
193-224
Main language of publication
English
Received
1995-08-08
Accepted
1997-09-22
Published
1998
Exact and natural sciences