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Persistence of form and the value group of reducible cubics
Author:
P. D. T. A. Elliott
Journal:
Trans. Amer. Math. Soc. 299 (1987), 133-143
MSC:
Primary 11N60; Secondary 11D85, 11K65
MathSciNet review:
869403
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Additional Information
Abstract: It is proved that the values of  ,  , at positive integers, multiplicatively generate the positive rationals. Analogs in rational function fields are obtained.
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A. Burgess, The distribution of quadratic residues and
non-residues, Mathematika 4 (1957), 106–112. MR 0093504
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A. Burgess, On character sums and primitive roots, Proc.
London Math. Soc. (3) 12 (1962), 179–192. MR 0132732
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A. Burgess, Dirichlet characters and polynomials, Proceedings
of the International Conference Number Theory (Moscow, 1971), 1973,
pp. 203–205, 266 (English, with Russian summary). MR 0401673
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P.
D. T. A. Elliott, Arithmetic functions and integer products,
Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of
Mathematical Sciences], vol. 272, Springer-Verlag, New York, 1985. MR 766558
(86j:11095)
- [5]
P.
D. T. A. Elliott, The value distribution of reducible cubics,
Canad. Math. Bull. 28 (1985), no. 3, 328–336.
MR 790954
(86h:11028), http://dx.doi.org/10.4153/CMB-1985-039-8
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P.
D. T. A. Elliott, On representing integers as products of integers
of a prescribed type, J. Austral. Math. Soc. Ser. A
35 (1983), no. 2, 143–161. MR 704421
(84m:10056)
- [7]
P.
D. T. A. Elliott, On the mean value of 𝑓(𝑝),
Proc. London Math. Soc. (3) 21 (1970), 28–96. MR 0266881
(42 #1783)
- [8]
R.
C. Vaughan, The Hardy-Littlewood method, Cambridge Tracts in
Mathematics, vol. 80, Cambridge University Press, Cambridge, 1981. MR 628618
(84b:10002)
- [1]
- D. A. Burgess, The distribution of quadratic residues and non-residues, Mathematika 4 (1957), 106-112. MR 0093504 (20:28)
- [2]
- -, On character sums and primitive roots, Proc. London Math. Soc. 12 (1962), 179-192. MR 0132732 (24:A2569)
- [3]
- -, Dirichlet characters and polynomials, Proc. Internat. Conf. in Number Theory (Moscow, 14-18 Sept. 1971), Trudy Mat. Inst. Steklov 132 (1973), 203-205. MR 0401673 (53:5500)
- [4]
- P. D. T. A. Elliott, Arithmetic functions and integer products, Grundlehren Math. Wiss., Springer-Verlag, New York and Berlin, 1984. MR 766558 (86j:11095)
- [5]
- -, The value distribution of reducible cubics, Canad. Math. Bull. 28 (1986), 328-336. MR 790954 (86h:11028)
- [6]
- -, On representing integers as products of integers of a prescribed type, J. Austral. Math. Soc. (Ser. A) 35 (1983), 143-161. MR 704421 (84m:10056)
- [7]
- -, On the mean value of
 , Proc. London Math. Soc. 21 (1970), 28-96. MR 0266881 (42:1783)
- [8]
- R. C. Vaughan, The Hardy-Littlewood method, Cambridge Univ. Press, London, 1981. MR 628618 (84b:10002)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1987-0869403-3
PII:
S 0002-9947(1987)0869403-3
Article copyright:
© Copyright 1987 American Mathematical Society
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