Lefschetz-Riemann-Roch theorem and coherent trace formula.
R.W. Thomason (1986)
Inventiones mathematicae
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R.W. Thomason (1986)
Inventiones mathematicae
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Marvin I. Knopp (1994)
Inventiones mathematicae
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S.M. Gonek (1984)
Inventiones mathematicae
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Nadj, Djerdji F. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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M.-C. Shaw (1985)
Inventiones mathematicae
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Masatoshi Suzuki (2013)
Acta Arithmetica
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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.
Lisa R. Goldberg (1994)
Inventiones mathematicae
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V. V. Mityushev (1997)
Annales Polonici Mathematici
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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.
Xiannan Li (2009)
Acta Arithmetica
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H.F. Baker (1894)
Mathematische Annalen
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Krzysztof Jarosz (2012)
Annales Polonici Mathematici
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The classical Riemann Mapping Theorem states that a nontrivial simply connected domain Ω in ℂ is holomorphically homeomorphic to the open unit disc 𝔻. We also know that "similar" one-dimensional Riemann surfaces are "almost" holomorphically equivalent. We discuss the same problem concerning "similar" domains in ℂⁿ in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem