Weak uniform distribution for divisor functions. I

Author:
Francis J. Rayner

Journal:
Math. Comp. **50** (1988), 335-342

MSC:
Primary 11N69; Secondary 11N37

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917839-9

MathSciNet review:
917839

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Narkiewicz (reference [3, pp. 204-205]) 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 with respect to a prime modulus,"*Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.*(LOMI), v. 93, 1980, pp. 218-224. (Russian) MR**579787 (81k:10068)****[2]**W. Narkiewicz, "Distribution of coefficients of Eisenstein series in residue classes,"*Acta Arith.*, v. 43, 1983, pp. 83-92. MR**730850 (85g:11086)****[3]**W. Narkiewicz, "Euler's function and the sum of divisors,"*J. Reine Angew. Math.*, v. 323, 1981, pp. 200-212. MR**611453 (82g:10077)****[4]**W. Narkiewicz,*Uniform Distribution of Sequences of Integers in Residue Classes*, Lecture Notes in Math., vol. 1087, Springer-Verlag, 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. 133-141. MR**678048 (84b:10070)****[6]**J. Sliwa, "On distribution of values of in residue classes,"*Colloq. Math.*, v. 28, 1973, pp. 283-291. MR**0327702 (48:6044)**

Retrieve articles in *Mathematics of Computation*
with MSC:
11N69,
11N37

Retrieve articles in all journals with MSC: 11N69, 11N37

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917839-9

Article copyright:
© Copyright 1988
American Mathematical Society