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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
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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
- T. M. Apostol, Introduction to analytic number theory, Springer (1984).
- B. Apostol and L. T´oth, Some remarks on regular integers modulo n, Filomat, 29 (2015) 687–701.
- I. Ege and E. Yyldyrym, Some generalized equalities for the q-gamma function, Filomat 26 (2012), 1227–1232.
- P. Haukkanen and L. T´oth, An analogue Ramanujan’s sum with respect to regular integers (mod r ), Ramanujan J., 27 (2012) 71–88.
- I. Kiuchi, M. Minamide and Y. Tanigawa, On a sum involving the M¨obius function, Acta Arith., 169 2 (2015) 149–168.
- P. J. McCarthy, Introduction to arithmetical functions, Springer (1986).
- S. S. Pillai, On an arithmetic function, J. Annamalai Univ., 2 (1937) 243–248.
- J. Singh, Defining power sums of n and φ(n) integers, Int. J. Number Theory, 5 (2009) 41–53.
- R. Sivaramakrishnan, Classical theory of arithmetic functions, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, 126 (1989).
- L. T´oth, Regular integers modulo n, Annales Univ. Sci. Budapest, Sect Comp., 29 (2008) 264–275.
- L. T´oth, A gcd-sum function over regular integers modulo n, J. Integer Sequences, 12 (2009) 8, Article 09.2.5.
- L. T´oth, A survey of gcd-sum functions, J. Integer Sequences, 13 (2010) 23, Article 10.8.1.
- L. T´oth, Menon’s identity and arithmetical sums representing functions of several variables, Rend. Semin. Mat. Univ. Politec. Torino, 69 (2011) 97–110.
- D. Zhang and W. Zhai, Mean values of a gcd-sum function over regular integer modulo mod n, J. Integer Sequences, 13 (2010) 11, Article 10.3.8.