The Experts below are selected from a list of 1293 Experts worldwide ranked by ideXlab platform
Kenneth S. Williams - One of the best experts on this subject based on the ideXlab platform.
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fourier series of a class of Eta quotients
International Journal of Number Theory, 2012Co-Authors: Kenneth S. WilliamsAbstract:The sum of divisors Function σ(m) is defined by Let denote the upper half of the complex plane. Let η(z) be the Dedekind Eta Function. A class of Eta quotients is given for which the Fourier series of each member of can be given explicitly. One example is where
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Values of the Dedekind Eta Function at Quadratic Irrationalities: Corrigendum
Canadian Journal of Mathematics, 2001Co-Authors: Alfred J. Van Der Poorten, Kenneth S. WilliamsAbstract:Habib Muzaffar of Carleton Universityhas pointed out to the authorsthat in their paper (A) only the result �K,d(x) + �K 1,d(x)= 1
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Values of the Dedekind Eta Function at Quadratic Irrationalities
Canadian Journal of Mathematics, 1999Co-Authors: Alfred J. Van Der Poorten, Kenneth S. WilliamsAbstract:Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that
Alfred J. Van Der Poorten - One of the best experts on this subject based on the ideXlab platform.
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Values of the Dedekind Eta Function at Quadratic Irrationalities: Corrigendum
Canadian Journal of Mathematics, 2001Co-Authors: Alfred J. Van Der Poorten, Kenneth S. WilliamsAbstract:Habib Muzaffar of Carleton Universityhas pointed out to the authorsthat in their paper (A) only the result �K,d(x) + �K 1,d(x)= 1
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Values of the Dedekind Eta Function at Quadratic Irrationalities
Canadian Journal of Mathematics, 1999Co-Authors: Alfred J. Van Der Poorten, Kenneth S. WilliamsAbstract:Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that
Michael S Milgram - One of the best experts on this subject based on the ideXlab platform.
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integral and series representations of riemann s zEta Function and dirichlet s Eta Function and a medley of related results
Journal of Mathematics, 2013Co-Authors: Michael S MilgramAbstract:Contour integral representations of Riemann's ZEta Function and Dirichlet's Eta (alternating ZEta) Function are presented and investigated. These representations flow naturally from methods developed in the 1800s, but somehow they do not appear in the standard reference summaries, textbooks, or literature. Using these representations as a basis, alternate derivations of known series and integral representations for the ZEta and Eta Function are obtained on a unified basis that differs from the textbook approach, and results are developed that appear to be new.
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integral and series representations of riemann s zEta Function dirichelet s Eta Function and a medley of related results
arXiv: Complex Variables, 2012Co-Authors: Michael S MilgramAbstract:Contour integral representations for Riemann's ZEta Function and Dirichelet's Eta (alternating ZEta) Function are presented and investigated. These representations flow naturally from methods developed in the 1800's, but somehow they do not appear in the standard reference summaries, textbooks or literature. Using these representations as a basis, alternate derivations of known series and integral representations for the ZEta and Eta Function are obtained on a unified basis that differs from the textbook approach, and results are developed that appear to be new.
Peter B. Gilkey - One of the best experts on this subject based on the ideXlab platform.
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invariance theory the heat equation and the atiyah singer index theorem
1995Co-Authors: Peter B. GilkeyAbstract:Pseudo-Differential Operators Introduction Fourier Transform and Sobolev Spaces Pseudo-Differential Operators on Rm Pseudo-Differential Operators on Manifolds Index of Fredholm Operators Elliptic Complexes Spectral Theory The Heat Equation Local Index Formula Variational Formulas Lefschetz Fixed Point Theorems The ZEta Function The Eta Function Characteristic Classes Introduction Characteristic Classes of Complex Bundles Characteristic Classes of Real Bundles Complex Projective Space Invariance Theory The Gauss-Bonnet Theorem Invariance Theory and Pontrjagin Classes Gauss-Bonnet for Manifolds with Boundary Boundary Characteristic Classes Singer's Question The Index Theorem Introduction Clifford Modules Hirzebruch Signature Formula Spinors The Spin Complex The Riemann-Roch Theorem K-Theory The Atiyah-Singer Index Theorem The Regularity at s = 0 of the Eta Function Lefschetz Fixed Point Formulas Index Theorem for Manifolds with Boundary The Eta Invariant of Locally Flat Bundles Spectral Geometry Introduction Operators of Laplace Type Isospectral Manifolds Non-Minimal Operators Operators of Dirac Type Manifolds with Boundary Other Asymptotic Formulas The Eta Invariant of Spherical Space Forms A Guide to the Literature Acknowledgment Introduction Bibliography Notation
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Residues of the Eta Function for an operator of Dirac type
Journal of Functional Analysis, 1992Co-Authors: Thomas Branson, Peter B. GilkeyAbstract:Abstract We compute the asymptotics of Tr L 2 ( Pe −tp 2 ) where P is a first order operator of Dirac type; this is equivalent to evaluating the residues of the Eta Function.
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Residues of the Eta Function for an operator of Dirac type with local boundary conditions
Differential Geometry and its Applications, 1992Co-Authors: Thomas Branson, Peter B. GilkeyAbstract:Abstract Let M be a compact manifold with smooth boundary. Let P be a first order operator of Dirac type on M with suitable local boundary conditions. We compute the asymptotics of Tr L 2 ( Pe - tP 2 ). This is equivalent to evaluating the residues of the Eta Function for the corresponding boundary value problem.
William Hart - One of the best experts on this subject based on the ideXlab platform.
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An identity for the Dedekind Eta-Function involving two independent complex variables
Bulletin of the London Mathematical Society, 2007Co-Authors: Bruce C. Berndt, William HartAbstract:The authors prove a new identity for the Dedekind Eta-Function that involves third powers of the Eta-Function, with each of the two cubes being a Function of a different complex variable.
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Evaluation of the Dedekind Eta Function
Canadian Mathematical Bulletin, 2006Co-Authors: Robin Chapman, William HartAbstract:Abstract. We extend the methods of Van der Poorten and Chapman for explicitly evaluating the Dedekind Eta Function at quadratic irrationalities. Via evaluation of Hecke L-series we obtain new evaluations at points in imaginary quadratic number fields with class numbers 3 and 4. Further, we overcome the limitations of the earlier methods and via modular equations provide explicit evaluations where the class number is 5 or 7.