ON THE MEAN-SQUARE FORMULA FOR THE RIEMANN ZETA-FUNCTION ON THE CRITICAL LINE

Authors
LAU YK
Citation
Yk. Lau, ON THE MEAN-SQUARE FORMULA FOR THE RIEMANN ZETA-FUNCTION ON THE CRITICAL LINE, Monatshefte fuer Mathematik, 117(1-2), 1994, pp. 103-106
Citations number
3
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Monatshefte fuer Mathematik → ACNP
ISSN journal
00269255
Volume
117
Issue
1-2
Year of publication
1994
Pages
103 - 106
Database
ISI
SICI code
0026-9255(1994)117:1-2<103:OTMFFT>2.0.ZU;2-F
Abstract
If u(n) denotes the nth zero of the function G(t):= integral-t/2 (E(u) - pi)du, t greater-than-or-equal-to 2, IVIC has shown that u(n+1) - u (n) << u(n)1/2 for all n and u(n+1) - u(n) >> u(n)1/2 (log u(n))-5 for infinitely many n. We sharpen his lower estimate for the gap u(n+1) - u(n) to the best possible, namely, u(n+1) - u(n) >> u(n)1/2 for infin itely many n.