Weak uniform distribution for divisor functions. I

Author:
Francis J. Rayner

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

MSC:
Primary 11N69; Secondary 11N37

MathSciNet review:
917839

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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 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****[2]**W. Narkiewicz,*Distribution of coefficients of Eisenstein series in residue classes*, Acta Arith.**43**(1983), no. 1, 83–92. MR**730850****[3]**W. Narkiewicz,*Euler’s function and the sum of divisors*, J. Reine Angew. Math.**323**(1981), 200–212. MR**611453**, 10.1515/crll.1981.323.200**[4]**Władysław Narkiewicz,*Uniform distribution of sequences of integers in residue classes*, Lecture Notes in Mathematics, vol. 1087, Springer-Verlag, Berlin, 1984. MR**766563****[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**, 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**

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

Article copyright:
© Copyright 1988
American Mathematical Society