Glasnik Matematicki, Vol. 33, No.1 (1998), 37-50.
CONVEXITY AND THE RIEMANN ζ-FUNCTION
Department of Mathematics, University of Hawaii, Honolulu, HI 96822,
Abstract. The convexity properties of the kernel
whose Fourier transform is the Riemann
investigated. In particular, it is shown that
is convex for t > 0. Also, lower bounds for the Turan
differences involving the moments of
are established. The paper concludes with several questions and
1991 Mathematics Subject Classification.
30D10, 30D15, 26A51.
Key words and phrases. Riemann hypothesis, convexity,
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