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Kiuchi, Isao
- Averages of Anderson-Apostol’s Sums
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Affiliations
1 Department of Mathematical Sciences, Yamaguchi University, Yoshida 1677-1, Yamaguchi-753-8512, JP
2 Onoda High School, Kushiyama 1-26-1, Sanyoonoda-753-0080, JP
1 Department of Mathematical Sciences, Yamaguchi University, Yoshida 1677-1, Yamaguchi-753-8512, JP
2 Onoda High School, Kushiyama 1-26-1, Sanyoonoda-753-0080, JP
Source
Journal of the Ramanujan Mathematical Society, Vol 31, No 4 (2016), Pagination: 339-357Abstract
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.
- A Mean Value Theorem for the Approximate Functional Equation of ζ2(s) for Short Intervals
Abstract Views :239 |
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Authors
Affiliations
1 Department of Mathematics, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, JP
2 Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, JP
1 Department of Mathematics, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, JP
2 Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, JP
Source
Journal of the Ramanujan Mathematical Society, Vol 15, No 1 (2000), Pagination: 53-70Abstract
As usual, let ((s) be the Riemann zeta-function, d{n) the number of positive divisors of n, k and I co-prime integers with 1 ≤ I ≤ k, and r = l/k.- Remarks on a Paper by B. Apostol and L. Toth
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Authors
Affiliations
1 Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, JP
2 Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, JP
1 Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, JP
2 Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, JP
Source
Journal of the Ramanujan Mathematical Society, Vol 34, No 1 (2019), Pagination: 43-57Abstract
We shall derive some formulas for partial sums of weighted averages over regular integers (mod n) of the generalized gcd-sum function with any arithmetical functions.References
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