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 -