Journal of the Ramanujan Mathematical Society

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Averages of Anderson-Apostol’s Sums


Affiliations
1 Department of Mathematical Sciences, Yamaguchi University, Yoshida 1677-1, Yamaguchi-753-8512, Japan
2 Onoda High School, Kushiyama 1-26-1, Sanyoonoda-753-0080, Japan
     

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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. Toth.
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  • Averages of Anderson-Apostol’s Sums

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Authors

Isao Kiuchi
Department of Mathematical Sciences, Yamaguchi University, Yoshida 1677-1, Yamaguchi-753-8512, Japan
Makoto Minamide
Department of Mathematical Sciences, Yamaguchi University, Yoshida 1677-1, Yamaguchi-753-8512, Japan
Masaaki Ueda
Onoda High School, Kushiyama 1-26-1, Sanyoonoda-753-0080, Japan

Abstract


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. Toth.