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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2000 Volume 269, Pages 151–163 (Mi znsl1312)

The Selberg $Z$-function and the Lindelöf conjecture

A. I. Vinogradov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: It is proved that, under some assumptions, the Selberg $Z$-function $Z(s)$ is of order $t^\varepsilon/(\sigma-\frac12)$ in a sufficiently small neighborhood of the critical straight line $\sigma>\frac12$, $t\ge1$, and $\varepsilon>0$ is an arbitrary small but fixed.

UDC: 517.9

Received: 24.12.1999


 English version:
Journal of Mathematical Sciences (New York), 2003, 115:1, 1969–1976

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