Search Results - General theory of automorphic functions of several complex variables

On Siegel’s product formulas for quadratic forms over algebraic number fields in higher dimensional cases: On Siegel's product formulas for quadratic forms over algebraic number fields in higher dimensional cases

Authors: Kojima, Hisashi Sakata, Hiroshi

Source: The Journal of Analysis. 33:619-646

Subject Terms: Analysis on other specific Lie groups, Quadratic forms over global rings and fields, theta series, Analytic theory (Epstein zeta functions, relations with automorphic forms and functions), Automorphic functions in symmetric domains, Theta series, Weil representation, theta correspondences, Siegel modular groups, Siegel and Hilbert-Siegel modular and automorphic forms, General theory of automorphic functions of several complex variables, automorphic forms, Siegel main theorem, analytic theory of quadratic forms, quadratic forms, Automorphic forms in several complex variables

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Access URL: https://zbmath.org/8035913
https://doi.org/10.1007/s41478-024-00850-0

On the Fourier coefficients of modular forms of several variables

Authors: Shimura, Goro

Source: Collected Papers ISBN: 9781461274056

Subject Terms: Theta series, Weil representation, theta correspondences, General theory of automorphic functions of several complex variables

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Access URL: https://zbmath.org/3519119

A Morera type theorem forL 2 functions in the Heisenberg group: A Morera type theorem for \(L^ 2\) functions in the Heisenberg group

Authors: Der-Chen Chang Mark Agranovsky Daniel Pascuas et al.

Source: Journal d’Analyse Mathématique. 57:282-296

Subject Terms: CR structures, CR operators, and generalizations, Morera type theorem, General theory of automorphic functions of several complex variables, 0101 mathematics, Heisenberg group, 01 natural sciences, \(CR\) functions

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Access URL: https://zbmath.org/221312
https://doi.org/10.1007/bf03041073
https://link.springer.com/article/10.1007%2FBF03041073

Automorphisms of nondegenerate CR quadrics and Siegel domains. Explicit description: Automorphisms of nondegenerate CR quadrics and Siegel domains. Explicit description.

Authors: Vladimir V. Ežov Gerd Schmalz Schmalz, Gerd

Contributors: Vladimir V. Ežov Gerd Schmalz Schmalz, Gerd

Source: The Journal of Geometric Analysis. 11:441-467

Subject Terms: automorphisms of quadrics, Siegel domains of second kind, General theory of automorphic functions of several complex variables, 0101 mathematics, Analysis on CR manifolds, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1007/BF02922014
https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3125210
https://hdl.handle.net/1959.8/41642

LOWER BOUNDS FOR L-FUNCTIONS AT THE EDGE OF THE CRITICAL STRIP.

Authors: Gelbart, Stephen S. Lapid, Erez M.

Source: American Journal of Mathematics; Jun2006, Vol. 128 Issue 3, p619-638, 20p

Subject Terms: NUMBER theory, L-functions, AUTOMORPHIC functions, FUNCTIONS of several complex variables, EISENSTEIN series, AUTOMORPHIC forms

THE ARCHIMEDEAN THEORY OF THE EXTERIOR SQUARE L-FUNCTIONS OVER ℚ.

Authors: Miller, Stephen D. Schmid, Wilfred

Source: Journal of the American Mathematical Society; Apr2012, Vol. 25 Issue 2, p465-506, 42p

Subject Terms: ARCHIMEDES' principle, L-functions, NUMBER theory, AUTOMORPHIC functions, FUNCTIONS of several complex variables

Note on Automorphic Functions of Several Variables: Note on automorphic functions of several variables

Authors: Carl Ludwig Siegel

Source: The Annals of Mathematics. 43:613

Subject Terms: Modular and automorphic functions, General theory of automorphic functions of several complex variables, modular functions, automorphic functions, almost periodic functions

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Access URL: https://zbmath.org/3107221
https://doi.org/10.2307/1968953
https://zbmath.org/3224738
https://doi.org/10.2307/1968953
http://www.jstor.org/stable/1968953?origin=crossref

Liftings and mean value theorems for automorphic L-functions.

Authors: Kohji Matsumoto

Source: Proceedings of the London Mathematical Society; Mar2005, Vol. 90 Issue 2, p297-320, 24p

Subject Terms: DIRICHLET series, AUTOMORPHIC functions, FUNCTIONS of several complex variables, SIEGEL domains, MODULAR forms, MATHEMATICAL forms

Reflection Operator and Canonical Basis.

Authors: Vinogradov, A. I.

Source: Journal of Mathematical Sciences; Jan2005, Vol. 125 Issue 2, p159-172, 14p

Subject Terms: AUTOMORPHIC functions, FUNCTIONS of several complex variables, HILBERT space, BANACH spaces, HYPERSPACE, SPECTRAL theory, MATHEMATICS

Composition theorems of \(S^p\) -weighted pseudo almost automorphic functions and applications

Authors: Tang, Chaohong Li, Hongxu

Subject Terms: Almost and pseudo-almost periodic solutions to ordinary differential equations, Composition theorem, semilinear differential equation, General theory of automorphic functions of several complex variables, \(S^p\) -weighted pseudo almost automorphic

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Access URL: https://zbmath.org/6611874

On the Kodaira dimension of the moduli space of abelian varieties

Authors: Tai, Yung-sheng

Source: Inventiones Mathematicae. 68:425-439

Subject Terms: extension of pluri-canonical differential forms, Kodaira dimension, Other groups and their modular and automorphic forms (several variables), General theory of automorphic functions of several complex variables, 01 natural sciences, Article, 510.mathematics, moduli space of principally polarized abelian varieties, Algebraic moduli problems, moduli of vector bundles, toroidal compactifications, moduli space of general type, Families, moduli, classification: algebraic theory, 0101 mathematics, Algebraic theory of abelian varieties

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Access URL: https://zbmath.org/3801719
https://doi.org/10.1007/bf01389411
https://link.springer.com/article/10.1007%2FBF01389411
https://link.springer.com/10.1007/BF01389411
http://ui.adsabs.harvard.edu/abs/1982InMat..68..425T/abstract
https://eudml.org/doc/142939

Multiplier systems for Hilbert's and Siegel's modular groups

Authors: Karl-Bernhard Gundlach

Source: Glasgow Mathematical Journal. 27:57-80

Subject Terms: factors of automorphy, subgroups of finite index, Theta series, Weil representation, theta correspondences, Automorphic forms on \(\mbox{GL}(2)\), Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms, Hilbert modular surfaces, multiplier systems, General theory of automorphic functions of several complex variables, weights, 0101 mathematics, 01 natural sciences, Hilbert modular group, Siegel modular group

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Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6499C4246B37B9F8DCEB1FD5C3243CA0/S0017089500006078a.pdf/div-class-title-multiplier-systems-for-hilbert-s-and-siegel-s-modular-groups-div.pdf
https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/multiplier-systems-for-hilberts-and-siegels-modular-groups/6499C4246B37B9F8DCEB1FD5C3243CA0
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0017089500006078
http://www.journals.cambridge.org/abstract_S0017089500006078

A property of new coordinates defining augmented Schottky spaces

Authors: Sato, Hiroki

Source: Nagoya Math. J. 88 (1982), 73-78

Subject Terms: Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), augmented Schottky spaces, 32G15, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Boundary behavior of holomorphic functions of several complex variables, General theory of automorphic functions of several complex variables, 0101 mathematics, boundary point, 01 natural sciences, 30F40, Schottky space of Riemann surfaces of genus g

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Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1186139BD0A621E4CDDDAC8F52BFEAD3/S0027763000020109a.pdf/div-class-title-a-property-of-new-coordinates-defining-augmented-schottky-spaces-div.pdf
https://www.cambridge.org/core/journals/nagoya-mathematical-journal/article/property-of-new-coordinates-defining-augmented-schottky-spaces/1186139BD0A621E4CDDDAC8F52BFEAD3
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1186139BD0A621E4CDDDAC8F52BFEAD3/S0027763000020109a.pdf/div-class-title-a-property-of-new-coordinates-defining-augmented-schottky-spaces-div.pdf
https://projecteuclid.org/download/pdf_1/euclid.nmj/1118787005
https://projecteuclid.org/euclid.nmj/1118787005
http://projecteuclid.org/euclid.nmj/1118787005

Beispiele dreidimensionaler Hilbertscher Modulmannigfaltigkeiten von allgemeinem Typ

Authors: Knöller, Friedrich Wilhelm

Source: Manuscripta Mathematica. 37:135-161

Subject Terms: totally real number field, Local complex singularities, 4. Education, Automorphic forms on \(\mbox{GL}(2)\), Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms, Hilbert modular surfaces, Moduli, classification: analytic theory, relations with modular forms, General theory of automorphic functions of several complex variables, 16. Peace & justice, 01 natural sciences, Article, 510.mathematics, surface of general type, defect of singularities, nonrationality of field of meromorphic functions, 0103 physical sciences, cusp, \(3\)-folds, 0101 mathematics, Hilbert modular varieties, Singularities of surfaces or higher-dimensional varieties, Global ground fields in algebraic geometry

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Access URL: https://eudml.org/doc/154834
https://link.springer.com/article/10.1007/BF01168507

Finiteness of a cohomology associated with certain Jackson integrals

Authors: Aomoto, Kazuhiko

Source: Tohoku Math. J. (2) 43, no. 1 (1991), 75-101

Subject Terms: Jackson integrals, Almost homogeneous manifolds and spaces, 33D80, 11F67, 32G20, General theory of automorphic functions of several complex variables, \(q\)-analogue, \(b\)-functions, 32S40, Theta functions and abelian varieties, Elliptic curves, difference system, Basic hypergeometric integrals and functions defined by them, 32N05

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Access URL: https://www.jstage.jst.go.jp/article/tmj1949/43/1/43_1_75/_article
https://projecteuclid.org/download/pdf_1/euclid.tmj/1178227537
https://www.projecteuclid.org/journals/tohoku-mathematical-journal/volume-43/issue-1/Finiteness-of-a-cohomology-associated-with-certain-Jackson-integrals/10.2748/tmj/1178227537.full
http://ci.nii.ac.jp/naid/110000026571
http://projecteuclid.org/euclid.tmj/1178227537

Holomorphic sections of line bundles over (H,C)-groups

Authors: Abe, Yukatika

Source: Manuscripta Mathematica. 60:379-385

Subject Terms: Analysis on real and complex Lie groups, 510.mathematics, holomorphic sections of line bundles, toroidal group, Sheaves and cohomology of sections of holomorphic vector bundles, general results, General theory of automorphic functions of several complex variables, 0101 mathematics, Complex Lie groups, group actions on complex spaces, quasi-abelian manifold, 01 natural sciences, Article

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Access URL: https://zbmath.org/4040304
https://doi.org/10.1007/bf01169345
https://link.springer.com/article/10.1007/BF01169345
https://link.springer.com/content/pdf/10.1007/BF01169345.pdf
https://eudml.org/doc/155286

Zur Begründung der Theorie der automorphen Funktionen in mehreren Variablen

Authors: EICHLER, M.

Source: Aequationes Mathematicae. 3:93-111

Subject Terms: Modular and automorphic functions, 510.mathematics, automorphic functions in several variables, Siegel modular groups, Siegel and Hilbert-Siegel modular and automorphic forms, General theory of automorphic functions of several complex variables, Article, Siegel modular forms

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Access URL: https://zbmath.org/3287092
https://doi.org/10.1007/bf01817503
https://eudml.org/doc/136002
https://link.springer.com/article/10.1007/BF01833510

Automorphe Abbildungen zu pseudokonkaven Gruppen

Authors: Wolfart, Jürgen

Source: Mathematische Annalen. 203:261-281

Subject Terms: 510.mathematics, 0103 physical sciences, General theory of automorphic functions of several complex variables, 0101 mathematics, 01 natural sciences, Article, Automorphic forms in several complex variables

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Access URL: https://link.springer.com/article/10.1007/BF01351907

Sphere Fibration Induced By Uniformtzation of Modular Group: Sphere fibration induced by uniformization of modular group

Authors: Harvey Cohn

Source: Journal of the London Mathematical Society. :10-20

Subject Terms: Automorphic forms on \(\mbox{GL}(2)\), Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms, Hilbert modular surfaces, General theory of automorphic functions of several complex variables, sphere fibration, uniformization, Hilbert modular group

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Access URL: https://zbmath.org/3263423
https://doi.org/10.1112/jlms/s1-43.1.10
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/s1-43.1.10

Some explicit resolutions of modular cusp singularities

Authors: Cohn, Harvey

Source: Mathematische Annalen. 198:123-130

Subject Terms: 510.mathematics, Removable singularities in several complex variables, General theory of automorphic functions of several complex variables, 0101 mathematics, 01 natural sciences, Article

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Access URL: https://eudml.org/doc/162297
https://link.springer.com/content/pdf/10.1007/BF01432282.pdf
https://link.springer.com/article/10.1007/BF01432282