Riemann’s function has an exponential bound

Beesack, Paul R.

doi:10.1090/S0002-9939-1983-0695265-5

Riemann’s function has an exponential bound
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Proc. Amer. Math. Soc. 88 (1983), 313-316 Request permission

Abstract:

The Riemann function $\upsilon (t;x)$ of a hyperbolic characteristic initial value problem has been much used in recent years to provide upper bounds for functions which satisfy Gronwall-type integral inequalities. This note gives a direct proof of the fact that $\upsilon$ satisfies an inequality of the form $\upsilon (t;x) \leqslant \exp (\int _t^x {b(s)ds}$.

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