On the Fourier series of the zeta-function logarithm on the vertical lines

A.M. Brydun; A.A. Kondratyuk

The Jensen-Littlewood theorem for a rectangle is generalized. The generalization is applied to the study of Fourier's series of the Riemann zeta-function logarithm on the vertical lines.

1. Littlewood J. E. On the zeros of the Riemann zeta-function, Proc. Cambr. Phil. Soc. 22 (1924), 295–318.

2. Titchmarsh J. C. The theory of the Riemann zeta-function, Second edition, Revised by D. R. Heath-Brown, Oxford, 1986.

3. Selberg A. Old and new conjectures and results about a class of Dirichlet series, in “Proceedings of the Amalfi Conference on Analytic Number Theory" (eds. E. Bombieri et al.), Università di Salerno, Salerno, 1992, 367–385; also Collected Papers (Vol. II), Springer Verlag, Berlin etc., 1991, 47–63.

4. Balazard M., $\rm{Ivi\check{c}}$ M. The mean square of logarithm of the zeta-function, Glasgow Math. J. 42 (2000), 157--166.

5. Kondratyuk A., Kshanovskyy I. On the logarithmic derivative of a meromorphic function, Matematychni Studii 21 (2004), no.1, 98–100.

	On the Fourier series of the zeta-function logarithm on the vertical lines
Author	A. M. Brydun, A. A. Kondratyuk a_kond@franko.lviv.ua, brydun@franko.lviv.ua Faculty of Mechanics and Mathematics,Lviv National University
Abstract	The Jensen-Littlewood theorem for a rectangle is generalized. The generalization is applied to the study of Fourier's series of the Riemann zeta-function logarithm on the vertical lines.
Keywords	Fourier series, zeta-function logarithm, vertical line
DOI	doi:10.30970/ms.22.1.97-104
Reference	1. Littlewood J. E. On the zeros of the Riemann zeta-function, Proc. Cambr. Phil. Soc. 22 (1924), 295–318. 2. Titchmarsh J. C. The theory of the Riemann zeta-function, Second edition, Revised by D. R. Heath-Brown, Oxford, 1986. 3. Selberg A. Old and new conjectures and results about a class of Dirichlet series, in “Proceedings of the Amalfi Conference on Analytic Number Theory" (eds. E. Bombieri et al.), Università di Salerno, Salerno, 1992, 367–385; also Collected Papers (Vol. II), Springer Verlag, Berlin etc., 1991, 47–63. 4. Balazard M., $\rm{Ivi\check{c}}$ M. The mean square of logarithm of the zeta-function, Glasgow Math. J. 42 (2000), 157--166. 5. Kondratyuk A., Kshanovskyy I. On the logarithmic derivative of a meromorphic function, Matematychni Studii 21 (2004), no.1, 98–100.
Pages	97-104
Volume	22
Issue	1
Year	2004
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html