Journal of the Ramanujan Mathematical Society
Volume 31, Issue 4, December 2016 pp. 339–357.
Averages of Anderson-Apostol's sums
Authors:
Isao Kiuchi (Yamaguchi), Makoto Minamide (Yamaguchi) and Masaaki Ueda (Sanyoonoda)
Author institution:Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, Japan
Summary:
We consider a weighted average for a generalized Anderson-Apostol
sum ∑ d|(k,n)f(d)g(k/d)h(n/d) for any
arithmetical functions f, g and h, with the weights
concerning completely multiplicative function, completely additive
function, logarithms, values of arithmetical functions for gcd's,
the Gamma function, the Bernoulli polynomials and binomial
coefficients, whose results are a generalization of
formulas due to E. Alkan and L. Tóth.
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