Concentration function of additive functions on shifted twin primes

• Autorzy: Simon Wong
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11N13: Primes in progressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 84
• Numer: 3
• Strony: 193-224

Daty

wydano

1998

otrzymano

1995-08-08

poprawiono

1997-09-22

Twórcy

autor

Simon Wong

• Department of Mathematical Sciences, Station #18, Eastern New Mexico University, Portales, New Mexico 88130, U.S.A.

Bibliografia

• [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.
• [3] P. D. T. A. Elliott, Multiplicative functions on arithmetic progressions. VI. More middle moduli, J. Number Theory 44 (1993), 178-208.
• [4] P. D. T. A. Elliott, The concentration function of additive functions on shifted primes, Acta Math. 173 (1994), 1-35.
• [5] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974.
• [6] H. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971.
• [7] I. Z. Ruzsa, On the concentration of additive functions, Acta Math. Acad. Sci. Hungar. 36 (1980), 215-232.
• [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).