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Volume 8, Issue 1 (2020), Pages [1] - [86]

AVERAGES OF FRACTIONAL PARTS 

[1] C. de la Vallée Poussin, Sur les valeurs moyennes de certaines functions arithmétiques, Annales de la Société Scientifique de Bruxelles 22 (1898), 84-90.

 

[2] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford, 1960.

 

[3] A. Ivić, The Riemann Zeta-Function, Dover, 2003.

 

[4] R. Jakimczuk, On the distribution of perfect powers, Journal of Integer Sequences 14 (2011), Article 11.8.5.

 

[5] R. Jakimczuk, A simple proof that the square-free numbers have density  Gulf Journal of Mathematics 1(2) (2013), 189-192.

 

[6] R. Jakimczuk, The kernel of powerful numbers, International Mathematical Forum 12(15) (2017), 721-730.

 

DOI: https://doi.org/10.12988/imf.2017.7759

 

[7] R. Jakimczuk, Functions of slow increase and integer sequences, Journal of Integer Sequences 13 (2010), Article 10.1.1.

 

[8] R. Jakimczuk, Composite numbers V, Applied Mathematical Sciences 13(9) (2019), 423-430.

 

DOI: https://doi.org/10.12988/ams.2019.9350

 

[9] F. Pillichshammer, Euler’s constant and averages of fractional parts, American Mathematical Monthly 117(1) (2010), 78-83.