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arithmetic series; Riemann zeta function; Möbius function

References:

[1] Chakraborty, K., Kanemitsu, S., Tsukada, H.: **Arithmetical Fourier series and the modular relation**. Kyushu J. Math. 66 (2012), 411-427. DOI 10.2206/kyushujm.66.411 | MR 3051345 | Zbl 1334.11072

[2] Davenport, H.: **On some infinite series involving arithmetical functions**. Q. J. Math., Oxf. Ser. 8 (1937), 8-13. DOI 10.1093/qmath/os-8.1.8 | Zbl 0016.20105

[3] Hardy, G. H., Littlewood, J. E.: **Contributions to the theory of the Riemann Zeta-function and the theory of the distribution of primes**. Acta Math. 41 (1917), 119-196 \99999JFM99999 46.0498.01. DOI 10.1007/BF02422942 | MR 1555148

[4] Hardy, G. H., Littlewood, J. E.: **Some problems of Diophantine approximation: The analytic properties of certain Dirichlet's series associated with the distribution of numbers to modulus unity**. Trans. Camb. Philos. Soc. 27 (1923), 519-534 \99999JFM99999 49.0131.01.

[5] Iwaniec, H., Kowalski, E.: **Analytic Number Theory**. Colloquium Publications. American Mathematical Society 53. American Mathematical Society, Providence (2004). DOI 10.1090/coll/053 | MR 2061214 | Zbl 1059.11001

[6] Li, H. L., Ma, J., Zhang, W. P.: **On some Diophantine Fourier series**. Acta Math. Sin., Engl. Ser. 26 (2010), 1125-1132. DOI 10.1007/s10114-010-8387-x | MR 2644050 | Zbl 1221.11060

[7] Luther, W.: **The differentiability of Fourier gap series and ``Riemann's example'' of a continuous, nondifferentiable function**. J. Approximation Theory 48 (1986), 303-321. DOI 10.1016/0021-9045(86)90053-5 | MR 0864753 | Zbl 0626.42008

[8] Paris, R. B., Kaminski, D.: **Asymptotics and Mellin-Barnes Integrals**. Encyclopedia of Mathematics and Its Applications 85. Cambridge University Press, Cambridge (2001). DOI 10.1017/CBO9780511546662 | MR 1854469 | Zbl 0983.41019

[9] Segal, S. L.: **On an identity between infinite series of arithmetic functions**. Acta Arith. 28 (1976), 345-348. DOI 10.4064/aa-28-4-345-348 | MR 0387222 | Zbl 0319.10050

[10] Titchmarsh, E. C.: **The Theory of the Riemann Zeta-Function**. Oxford Science Publications. Oxford University Press, Oxford (1986). MR 0882550 | Zbl 0601.10026