Open AccessFourier coefficients associated with the Riemann zeta-function
Author(s) -
Yu. V. Basiuk,
S. I. Tarasyuk
Publication year - 2016
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.8.1.16-20
Subject(s) - riemann zeta function , mathematics , riemann hypothesis , fourier series , critical line , riemann xi function , prime zeta function , arithmetic zeta function , kernel (algebra) , series (stratigraphy) , mathematical analysis , pure mathematics , physics , thermodynamics , paleontology , biology
We study the Riemann zeta-function $\zeta(s)$ by a Fourier series method. The summation of $\log|\zeta(s)|$ with the kernel $1/|s|^{6}$ on the critical line $\mathrm{Re}\; s = \frac{1}{2}$ is the main result of our investigation. Also we obtain a new restatement of the Riemann Hypothesis.