Weak uniform distribution for divisor functions. I
Author:
Francis J. Rayner
Journal:
Math. Comp. 50 (1988), 335342
MSC:
Primary 11N69; Secondary 11N37
MathSciNet review:
917839
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Abstract: Narkiewicz (reference [3, pp. 204205]) has proposed an algorithm for determining the moduli with respect to which a given arithmetic function (of suitable type) has weak uniform distribution. The class of functions to which this algorithm applies includes the divisor functions . The present paper gives an improvement to the algorithm for odd values of i, which makes computation feasible for values of i up to 200. The results of calculations for odd values of i in the range are reported.
 [1]
O.
M. Fomenko, The distribution of values of multiplicative functions
modulo a prime number, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst.
Steklov. (LOMI) 93 (1980), 218–224, 229 (Russian).
Studies in number theory, 6. MR 579787
(81k:10068)
 [2]
W.
Narkiewicz, Distribution of coefficients of Eisenstein series in
residue classes, Acta Arith. 43 (1983), no. 1,
83–92. MR
730850 (85g:11086)
 [3]
W.
Narkiewicz, Euler’s function and the sum of divisors, J.
Reine Angew. Math. 323 (1981), 200–212. MR 611453
(82g:10077), http://dx.doi.org/10.1515/crll.1981.323.200
 [4]
Władysław
Narkiewicz, Uniform distribution of sequences of integers in
residue classes, Lecture Notes in Mathematics, vol. 1087,
SpringerVerlag, Berlin, 1984. MR 766563
(86g:11014)
 [5]
W.
Narkiewicz and F.
Rayner, Distribution of values of 𝜎₂(𝑛) in
residue classes, Monatsh. Math. 94 (1982),
no. 2, 133–141. MR 678048
(84b:10070), http://dx.doi.org/10.1007/BF01301931
 [6]
Jan
Śliwa, On distribution of values of 𝜎(𝑛) in
residue classes, Colloq. Math. 27 (1973),
283–291, 332. MR 0327702
(48 #6044)
 [1]
 O. M. Fomenko, "The distribution of values of multiplicative functions with respect to a prime modulus," Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), v. 93, 1980, pp. 218224. (Russian) MR 579787 (81k:10068)
 [2]
 W. Narkiewicz, "Distribution of coefficients of Eisenstein series in residue classes," Acta Arith., v. 43, 1983, pp. 8392. MR 730850 (85g:11086)
 [3]
 W. Narkiewicz, "Euler's function and the sum of divisors," J. Reine Angew. Math., v. 323, 1981, pp. 200212. MR 611453 (82g:10077)
 [4]
 W. Narkiewicz, Uniform Distribution of Sequences of Integers in Residue Classes, Lecture Notes in Math., vol. 1087, SpringerVerlag, Berlin and New York, 1984. MR 766563 (86g:11014)
 [5]
 W. Narkiewicz & F. Rayner, "Distribution of values of in residue classes," Monatsh. Math., v. 94, 1982, pp. 133141. MR 678048 (84b:10070)
 [6]
 J. Sliwa, "On distribution of values of in residue classes," Colloq. Math., v. 28, 1973, pp. 283291. MR 0327702 (48:6044)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198809178399
PII:
S 00255718(1988)09178399
Article copyright:
© Copyright 1988 American Mathematical Society
