TY - GEN
T1 - On the Sign of the Real Part of the Riemann Zeta Function
AU - de Reyna, Juan Arias
AU - Brent, Richard P.
AU - van de Lune, Jan
PY - 2013
Y1 - 2013
N2 - We consider the distribution of the argument of the Riemann zeta function on vertical lines with real part greater than 1/2, and in particular two densities related to the argument and to the real part of the zeta function on such lines. Using classical results of Bohr and Jessen, we obtain an explicit expression for the characteristic function associated with the argument. We give explicit expressions for the densities in terms of this characteristic function. Finally, we give a practical algorithm for evaluating these expressions to obtain accurate numerical values of the densities.
AB - We consider the distribution of the argument of the Riemann zeta function on vertical lines with real part greater than 1/2, and in particular two densities related to the argument and to the real part of the zeta function on such lines. Using classical results of Bohr and Jessen, we obtain an explicit expression for the characteristic function associated with the argument. We give explicit expressions for the densities in terms of this characteristic function. Finally, we give a practical algorithm for evaluating these expressions to obtain accurate numerical values of the densities.
UR - http://www.scopus.com/inward/record.url?scp=84883321548&partnerID=8YFLogxK
U2 - 10.1007/978-1-4614-6642-0_3
DO - 10.1007/978-1-4614-6642-0_3
M3 - Conference contribution
SN - 9781461466413
T3 - Springer Proceedings in Mathematics and Statistics
SP - 75
EP - 97
BT - Number Theory and Related Fields
PB - Springer New York LLC
ER -