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Additive functions on shifted primes
Author(s):
P. D. T. A.
Elliott
Journal:
Bull. Amer. Math. Soc.
27
(1992),
273-278.
MSC (2000):
Primary 11N37;
Secondary 11K65, 11L20
MathSciNet review:
1155279
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Additional information
Abstract:
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.
References:
-
- [1]
- P.D.T.A. Elliott, Multiplicative functions on arithmetic progressions, Mathematika 34 (1987), 199-206. MR 933499 (89g:11083)
- [2]
- -, Extrapolating the mean-values of multiplicative functions, Nederl. Akad. Wetensch. Proc. Ser. A 92 (1989), 409-420. MR 1041494 (91a:11043)
- [3]
- -, Multiplicative functions on arithmetic progressions III: The large moduli, A tribute to Paul Erdös (A. Baker, B. Bollobás, and A. Hajnal, eds.), Cambridge Univ. Press Cambridge, 1990, pp. 177-194. MR 1117012 (92g:11092)
- [4]
- -, Multiplicative functions on arithmetic progressions IV: The middle moduli, J. London Math. Soc. (2) 41 (1990), 201-216. MR 1067262 (91m:11075)
- [5]
- -, Multiplicative functions on arithmetic progressions V: Composite moduli, J. London Math. Soc. (2) 41 (1990), 408-424. MR 1072058 (91m:11076)
- [6]
- -, Multiplicative functions on arithmetic progressions VI: More middle moduli, J. Number Theory (to appear). MR 1225952 (94i:11073)
- [7]
- P. Erdös and A. Wintner, Additive arithmetical functions and statistical independence, Amer. J. Math. 61 (1939), 713-721. MR 0000247 (1:40c)
- [8]
- G. Halász, On the distribution of additive arithmetical functions, Acta Arith. 27 (1975), 143-152.
- [9]
- I. Z. Ruzsa, On the concentration of additive functions, Acta Math. Hungar. 36 (1980), 215-232. MR 612193 (82j:10088)
- [10]
- N. M. Timofeev, The Erdös-Kubilius conjecture concerning the value distribution of additive functions on the sequence of shifted primes, Acta Arith. LVIII (1991), 113-131. (Russian) MR 1121073 (92i:11105)
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Additional Information:
DOI:
10.1090/S0273-0979-1992-00317-8
PII:
S 0273-0979(1992)00317-8
Copyright of article:
Copyright
1992,
American Mathematical Society
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