a1 Department of Mathematics, Davidson College, Davidson, NC, 28035-6996, USA (email: [email protected])
a2 Department of Mathematics and Computer Science, University of Lethbridge, Alberta, Canada T1K 3M4 (email: [email protected])
We investigate the behaviour of the function, where is the Liouville function and is a real parameter. The case where was investigated by Pólya; the case , by Turán. The question of the existence of sign changes in both of these cases is related to the Riemann hypothesis. Using both analytic and computational methods, we investigate similar problems for the more general family , where , and their relationship to the Riemann hypothesis and other properties of the zeros of the Riemann zeta function. The case where is of particular interest.
(Received May 06 2011)
(Accepted February 01 2012)
(Online publication September 27 2012)
2010 Mathematics subject classification
Keywords and phrases
Dedicated to the memory of Alf van der Poorten
Communicated by I. E. Shparlinski
This work was partially supported by a grant from the Simons Foundation (#210069 to M. Mossinghoff).