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The Erdős-Kac theorem for polynomials of several variables
Author(s):
Maosheng
Xiong
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2601-2608.
MSC (2000):
Primary 11N64, 11R09
Posted:
February 11, 2009
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Abstract:
We prove two versions of the Erdős-Kac type theorem for polynomials of several variables on some varieties arising from translation and affine linear transformation.
References:
-
- 1.
- K. Alladi, An Erdős-Kac theorem for integers without large prime factors, Acta Arith. 49(1987), no. 1, 81-105. MR 913766 (89b:11077)
- 2.
- J. Bourgain, A. Gamburd, Uniform expansion bounds for Cayley graphs of
, Annals of Mathematics (2) 167 (2008), 625-642. MR 2415383 - 3.
- J. Bourgain, A. Gamburd, P. Sarnak, Sieving, expanders, and sum-product, preprint.
- 4.
- A. Cafurea, G Materab, Improved explicit estimates on the number of solutions of equations over a finite field, Finite Fields and Their Applications 12(2006), 155-185. MR 2206396 (2006k:11117)
- 5.
- N. G. Chebotarev, Opredelenie plotnosti sovokupnosti prostykh chisel, prinadlezhashchikh zadannomu klassu podstanovok, Izv. Ross. Akad. Nauk. 17(1923), 205-250.
- 6.
- P. D. T. A. Elliott, Probabilistic Number Theory, I & II. Grundlehren Math. Wiss., vols. 239 and 240, Springer, New York, 1979. MR 551361 (82h:10002a), MR 0560507 (82h:10002b)
- 7.
- P. Erdős, M. Kac, The Gaussian law of errors in the theory of additive number theoretic functions, Amer. J. Math. 62(1940), 738-742. MR 0002374 (2:42c)
- 8.
- A. Granville, K. Soundararajan, Sieving and the Erdős-Kac theorem, Equidistribution in Number Theory, an Introduction, 15-27, NATO Sci. Ser. II Math. Phys. Chem., 237, Springer, Dordrecht, 2007. MR 2290492 (2008b:11103)
- 9.
- H. Halberstam, On the distribution of additive number theoretic functions, II, J. London Math. Soc. 31(1956), 1-14. MR 0073626 (17:461d)
- 10.
- G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number
, Quart. J. Pure Appl. Math. 48(1917), 76-97. - 11.
- H. Hwang, On convergence rates in the central limit theorems for combinatorial structures, European J. Combin. 19(1998), no. 3, 329-343. MR 1621021 (99c:60014)
- 12.
- S. Lang, A. Weil, Number of points of varieties in finite fields, Amer. J. Math. 76 (1954), 819-827. MR 0065218 (16:398d)
- 13.
- Y. Liu, Prime divisors of the number of rational points on elliptic curves with complex multiplication, Bull. London Math. Soc. 37(2005), 658-664. MR 2164827 (2006h:11058)
- 14.
- Y. Liu, A generalization of the Erdős-Kac theorem and its applications, Canad. Math. Bull. 47(2004), no. 4, 589-606. MR 2099756 (2005i:11138b)
- 15.
- Y. Liu, Prime analogues of the Erdős-Kac theorem for elliptic curves, J. Number Theory 119(2006), no. 2, 155-170. MR 2250042 (2007e:11066)
- 16.
- R. Murty, K. Murty, An analogue of the Erdős-Kac theorem for Fourier coefficients of modular forms, Indian J. Pure Appl. Math. 15(1984), no. 10, 1090-1101. MR 765015 (86d:11039)
- 17.
- R. Murty, F. Saidak, Non-abelian generalizations of the Erdős-Kac theorem, Canad. J. Math. 56(2004), no. 2, 356-372. MR 2040920 (2005a:11114)
- 18.
- E. Noether, Ein algebraisches Kriterium für absolute Irreduzibilität, Mathematische Annalen 85(1922), 26-40. MR 1512042
- 19.
- F. Saidak, New Erdős-Kac type theorems, Arch. Math. (Basel) 85(2005), no. 4, 345-361. MR 2174232 (2006g:11156)
- 20.
- J. Thuswaldner, R. Tichy, An Erdős-Kac theorem for systems of
-additive functions, Indag. Math. (N.S.) 11(2000), no. 2, 283-291. MR 1813728 (2002e:11106) - 21.
- P. Turán, On a theorem of Hardy and Ramanujan, J. London Math. Soc. 9(1934), 274-276.
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Additional Information:
Maosheng
Xiong
Affiliation:
Department of Mathematics, Eberly College of Science, Pennsylvania State University, McAllister Building, University Park, Pennsylvania 16802
Email:
xiong@math.psu.edu
DOI:
10.1090/S0002-9939-09-09830-X
PII:
S 0002-9939(09)09830-X
Received by editor(s):
March 20, 2008,
Received by editor(s) in revised form:
October 31, 2008
Posted:
February 11, 2009
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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