@article{bwmeta1.element.bwnjournal-article-aav75i1p39bwm, author = {U. Balakrishnan and Y.-F. S. P\'etermann}, title = {The Dirichlet series of $$\zeta$(s)$\zeta$^$\alpha$(s+1)f(s+1)$: On an error term associated with its coefficients}, journal = {Acta Arithmetica}, volume = {76}, year = {1996}, pages = {39-69}, zbl = {0846.11054}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav75i1p39bwm} }
U. Balakrishnan; Y.-F. S. Pétermann. The Dirichlet series of $ζ(s)ζ^α(s+1)f(s+1)$: On an error term associated with its coefficients. Acta Arithmetica, Tome 76 (1996) pp. 39-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav75i1p39bwm/
[000] [1] U. Balakrishnan, On the sum of divisors function, J. Number Theory 51 (1995), 147-168. | Zbl 0823.11052
[001] [2] S. D. Chowla, An order result involving Euler's ϕ-function, J. Indian Math. Soc. 18 (1929/30), 138-141. | Zbl 55.0106.03
[002] [3] P. Codecà, On the properties of oscillations and almost periodicity of certain convolutions, Rend. Sem. Mat. Univ. Padova 71 (1984), 373-387. | Zbl 0552.10030
[003] [4] P. J. G. L. Dirichlet, Ueber die Bestimmung der mittleren Werthe in der Zahlentheorie, Abh. Kön. Preuss. Akad. (1849), 69-83; Also in: Werke, II, Berlin, 1897, 51-66.
[004] [5] P. Erdős and H. N. Shapiro, On the changes of sign of a certain error function, Canad. J. Math. 3 (1951), 375-385. | Zbl 0044.03903
[005] [6] I. I. Il’yasov, Estimate of the remainder term of the sum , Izv. Akad. Nauk Kazakh. SSR Ser. Fiz.-Mat. 1969 (3), 77-79 (in Russian).
[006] [7] A. Ivić, The Riemann Zeta-function, Wiley, 1985. | Zbl 0556.10026
[007] [8] E. Landau, Ueber die zahlentheoretische Funktion ϕ(n) und ihre Beziehung zur Goldbachschen Satz, Gött. Nachr. (1900), 177-186.
[008] [9] H. L. Montgomery, Fluctuations in the mean of Euler's phi function, Proc. Indian Acad. Sci. Math. Sci. 97 (1987), 239-245. | Zbl 0656.10042
[009] [10] Y.-F. S. Pétermann, An Ω-theorem for an error term related to the sum-of-divisors function, Monatsh. Math. 103 (1987), 145-157; Addendum, Proc. Indian Acad. Sci. Math. Sci. 104 (1988), 193-194.
[010] [11] Y.-F. S. Pétermann, About a theorem of Paolo Codecà's and Ω-estimates for arithmetical convolutions, J. Number Theory 30 (1988), 71-85; Addendum, J. Number Theory 36 (1990), 322-327. | Zbl 0649.10034
[011] [12] H. Rademacher, Topics in Analytic Number Theory, Grundlehren Math. Wiss. 169, Springer, New York, 1973. | Zbl 0253.10002
[012] [13] S. Ramanujan, Some formulae in the theory of numbers, Mess. Math. 45 (1916), 81-84; also in: Collected Papers, Cambridge University Press, 1927.
[013] [14] V. Schemmel, Ueber relative Primzahlen, J. Reine Angew. Math. 70 (1869), 191-192.
[014] [15] R. Sitaramachandrarao, On an error term of Landau, Indian J. Pure Appl. Math. 13 (1982), 882-885. | Zbl 0494.10033
[015] [16] A. Sivaramasarma, Some problems in the theory of Farey series and the Euler totient function, Doctoral thesis (Chapter 8), Waltair, 1979.
[016] [17] R. A. Smith, An error term of Ramanujan, J. Number Theory 2 (1970), 91-96. | Zbl 0188.10401
[017] [18] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Institut Elie Cartan 13, 1990.
[018] [19] A. Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Deutsch. Verlag der Wiss., Berlin, 1963. | Zbl 0146.06003
[019] [20] S. Wigert, Sur quelques fonctions arithmétiques, Acta Math. 37 (1914), 113-140. | Zbl 45.0328.01