Glasnik Matematicki, Vol. 33, No.1 (1998), 37-50.
CONVEXITY AND THE RIEMANN ζ-FUNCTION
George Csordas
Department of Mathematics, University of Hawaii, Honolulu, HI 96822,
USA
e-mail: george@math.hawaii.edu
Abstract. The convexity properties of the kernel
Φ(t)
whose Fourier transform is the Riemann
ζ-function are
investigated. In particular, it is shown that
Φ(√t)
is convex for t > 0. Also, lower bounds for the Turan
differences involving the moments of
Φ(t)
are established. The paper concludes with several questions and
open problems.
1991 Mathematics Subject Classification.
30D10, 30D15, 26A51.
Key words and phrases. Riemann hypothesis, convexity,
moments.
Full text (PDF) (free access)
Glasnik Matematicki Home Page