Geodesic
The Atkinson type formula for the periodic zeta-function
Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 180-199.

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In the paper an explicit formula for the error term in the average mean square formula for the periodic zeta-function with rational parameter in the critical strip is obtained.
Keywords: Atkinson formula, generalized divisor function, periodic zeta-function. 
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S. Černigova; A. Laurinčikas. The Atkinson type formula for the periodic zeta-function. Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 180-199. http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a17/

[1] Atkinson F. V., “The mean-value of the Riemann zeta function”, Acta Math., 81 (1949), 353–376 | DOI | MR | Zbl

[2] Hafner J. L., “On the representation of the summatory functions of a class of arithmetical functions”, Analytic Number Theory, Lecture Notes in Mathematics, 899, 1981, 148–165 | DOI | MR | Zbl

[3] Heath-Brown D. R., “The twelfth power moment of the Riemann zeta-function”, Quart. J. Math. Oxford, 29 (1978), 443–462 | DOI | MR | Zbl

[4] Ivič A., The Riemann zeta-function: The Theory of the Riemann zeta-function with applications, Wiley, New York, 1985 | MR | Zbl

[5] Jutila M., “Transformation formulae for Dirichlet polynomials”, J. Number Theory, 18 (1984), 135–156 | DOI | MR | Zbl

[6] Jutila M., “Atkinson's formula revisited”, Voronoi's Impact on Modern Science, Book 1, Proc. Inst. Math. National Acad. Sc. Ukraine, 14, Kiev, 1998, 137–154

[7] Karaliūnaitė J., “The Atkinson formula for the periodic zeta-function in the central strip”, Voronoi's Impact on Modern Science, Proceedings of the 4th International Conference on Analytic Number Theory and Spatial Tessellations, Book 4, v. 1, Institute of Mathematics, NAS of Ukraine, Kyiv, 2008, 48–58

[8] Karaliūnaitė J., Laurinčikas A., “The Atkinson formula for the periodic zeta-function”, Lith. matem. J., 47:3 (2007), 504–516 | MR

[9] Laurinčikas A., “The Atkinson formula near the critical line”, Analytic and Probabilistic Methods in Number Theory, New Trends in Probability and Statistics, 2, TEV, Vilnius; VSP, Utrecht, 1992, 335–354 | MR

[10] Laurinčikas A., “The Atkinson formula near the critical line, II”, Liet. Math. Rinkinys., 33:3 (1993), 302–313 | MR | Zbl

[11] Matsumoto K., “The mean square of the Riemann zeta-function in the critical strip”, Japan J. Math., 15:1 (1989), 1–13 | MR | Zbl

[12] Matsumoto K., Meurman T., “The mean square of the Riemann zeta-function in the critical strip, III”, Acta Math., 64:4 (1993), 357–382 | MR | Zbl

[13] Meurman T., “A generalization of Atkinson's formula to $L$-functions”, Acta Arithm., 47 (1986), 351–370 | MR | Zbl

[14] Meurman T., “On the mean square of the Riemann zeta-function”, Quart. J. Math. Oxford (2), 38 (1987), 337–343 | DOI | MR | Zbl

[15] Motohashi Y., “A note on the mean value of the zeta and $L$-functions, IV”, Proc. Japan Acad., 62A (1986), 311–313 | MR | Zbl

[16] Oppenheim A., “Some identities in the theory of numbers”, Proc. London Math. Soc. (2), 26 (1927), 295–350 | DOI | MR | Zbl