A relation between the Riemann zeta-function and the hyperbolic laplacian
Yoichi Motohashi (1995)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Yoichi Motohashi (1995)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Isao Kiuchi, Yoshio Tanigawa (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.
Filip Saidak, Peter D. Zvengrowski (2003)
Mathematica Slovaca
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Andreas Guthmann (1997)
Acta Arithmetica
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Introduction. The recent discovery of an analogue of the Riemann-Siegel integral formula for Dirichlet series associated with cusp forms [2] naturally raises the question whether similar formulas might exist for other types of zeta functions. The proof of these formulas depends on the functional equation for the underlying Dirichlet series. In both cases, for ζ(s) and for the cusp form zeta functions, only a simple gamma factor is involved. The next simplest case arises when two such...
André Voros (2003)
Annales de l’institut Fourier
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A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.
Aleksandar Ivić (2003)
Journal de théorie des nombres de Bordeaux
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For a fixed integer , and fixed we consider where is the error term in the above asymptotic formula. Hitherto the sharpest bounds for are derived in the range min . We also obtain new mean value results for the zeta-function of holomorphic cusp forms and the Rankin-Selberg series.