On subspaces of Riemann-Otsuki space.
Nadj, Djerdji F. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Nadj, Djerdji F. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.
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The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.
Pingzhi Yuan, Jiagui Luo (2010)
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