DLMF: Untitled Document

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P. Bleher and A. Its (1999) Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. (2) 150 (1), pp. 185–266.

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External Links:: ISSN 0003-486X, Document, MathReview (Thomas Kriecherbauer), ZentralBlatt
Referenced by:: §18.32.
Encodings:: BibTeX

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Random Matrix Theory

►Hermite polynomials (and their Freud-weight analogs (§18.32)) play an important role in random matrix theory. … ►

Riemann–Hilbert Problems

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H. E. Rauch and A. Lebowitz (1973) Elliptic Functions, Theta Functions, and Riemann Surfaces. The Williams & Wilkins Co., Baltimore, MD.

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External Links:: MathReview (H. H. Martens), ZentralBlatt
Referenced by:: §20.11(iv), §20.12(ii).
Encodings:: BibTeX

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D. St. P. Richards (2004) Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.

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External Links:: ISSN 0022-4715, Document, MathReview (Stamatis Koumandos), ZentralBlatt
Referenced by:: §35.9.
Encodings:: BibTeX

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B. Riemann (1859) Über die Anzahl der Primzahlen unter einer gegebenen Grösse. Monats. Berlin Akad. November 1859, pp. 671–680.

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Notes:: Reprinted in Gesammelte Mathematische Werke, pp. 145–155, published by Dover Publications, New York, N.Y. 1953.
Referenced by:: §25.1, (25.2.1), §25.2(i).
Encodings:: BibTeX

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B. Riemann (1899) Elliptische Functionen. Teubner, Leipzig.

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Notes:: Based on notes of lectures by B. Riemann edited and published by H. Stahl. Reprinted by UMI Books on Demand (Ann Arbor, MI, USA).
External Links:: ZentralBlatt
Referenced by:: §20.12(ii).
Encodings:: BibTeX

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B. Riemann (1851) Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse. Inauguraldissertation, Göttingen.

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Referenced by:: §21.7(i).
Encodings:: BibTeX

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B. K. Choudhury (1995) The Riemann zeta-function and its derivatives. Proc. Roy. Soc. London Ser. A 450, pp. 477–499.

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External Links:: ISSN 0962-8444, FullText, MathReview, ZentralBlatt
Referenced by:: §25.18(i).
Encodings:: BibTeX

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W. J. Cody, K. E. Hillstrom, and H. C. Thacher (1971) Chebyshev approximations for the Riemann zeta function. Math. Comp. 25 (115), pp. 537–547.

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External Links:: ISSN 0025-5718, FullText, MathReview, ZentralBlatt
Referenced by:: 1st item.
Encodings:: BibTeX

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A. Cruz, J. Esparza, and J. Sesma (1991) Zeros of the Hankel function of real order out of the principal Riemann sheet. J. Comput. Appl. Math. 37 (1-3), pp. 89–99.

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External Links:: ISSN 0377-0427, Document, MathReview (Boro Döring), ZentralBlatt
Referenced by:: §10.21(ix).
Encodings:: BibTeX

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A. Csótó and G. M. Hale (1997)

S

-matrix and

R

-matrix determination of the low-energy

{}^{5}\mathrm{He}

and

{}^{5}\mathrm{Li}

resonance parameters. Phys. Rev. C 55 (1), pp. 536–539.

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External Links:: Document
Referenced by:: 2nd item.
Encodings:: BibTeX

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… ►First, as spherical functions on noncompact Riemannian symmetric spaces of rank one, but also as associated spherical functions, intertwining functions, matrix elements of SL

(2,\mathbb{R})

, and spherical functions on certain nonsymmetric Gelfand pairs. … ►The three singular points in Riemann’s differential equation (15.11.1) lead to an interesting Riemann sheet structure. By considering, as a group, all analytic transformations of a basis of solutions under analytic continuation around all paths on the Riemann sheet, we obtain the monodromy group. These monodromy groups are finite iff the solutions of Riemann’s differential equation are all algebraic. …

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G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris (1994) Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.

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External Links:: Document
Referenced by:: §13.28(iii).
Encodings:: BibTeX

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N. G. de Bruijn (1937) Integralen voor de

\zeta

-functie van Riemann. Mathematica (Zutphen) B5, pp. 170–180 (Dutch).

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Notes:: In Dutch.
External Links:: ZentralBlatt
Referenced by:: (25.5.15), (25.5.16), (25.5.17), (25.5.18), (25.5.19), §25.5(ii).
Encodings:: BibTeX

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B. Deconinck and M. van Hoeij (2001) Computing Riemann matrices of algebraic curves. Phys. D 152/153, pp. 28–46.

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External Links:: ISSN 0167-2789, Document, MathReview (John B. Little), ZentralBlatt
Referenced by:: 3rd item.
Encodings:: BibTeX

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T. M. Dunster (2006) Uniform asymptotic approximations for incomplete Riemann zeta functions. J. Comput. Appl. Math. 190 (1-2), pp. 339–353.

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External Links:: ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt
Referenced by:: §8.22(ii).
Encodings:: BibTeX

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A. J. Durán and F. A. Grünbaum (2005) A survey on orthogonal matrix polynomials satisfying second order differential equations. J. Comput. Appl. Math. 178 (1-2), pp. 169–190.

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External Links:: ISSN 0377-0427, Document, MathReview, ZentralBlatt
Referenced by:: §18.36(iv).
Encodings:: BibTeX

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	Open Source									With Book		Commercial
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25.21(ii) $\zeta\left(s\right)$ , $s\in\mathbb{R}$	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓		✓	✓	✓
25.21(iii) $\zeta\left(s\right)$ , $s\in\mathbb{C}$	✓			✓			✓	✓	✓	✓			✓	✓	✓
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35 Functions of Matrix Argument
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H. A. Yamani and L. Fishman (1975)

J

-matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering. J. Math. Phys. 16, pp. 410–420.

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Referenced by:: §18.39(iv).
Encodings:: BibTeX

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A. Yu. Yeremin, I. E. Kaporin, and M. K. Kerimov (1985) The calculation of the Riemann zeta function in the complex domain. USSR Comput. Math. and Math. Phys. 25 (2), pp. 111–119.

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External Links:: Document, ZentralBlatt
Referenced by:: §25.18(i).
Encodings:: BibTeX

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A. Yu. Yeremin, I. E. Kaporin, and M. K. Kerimov (1988) Computation of the derivatives of the Riemann zeta-function in the complex domain. USSR Comput. Math. and Math. Phys. 28 (4), pp. 115–124.

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Notes:: Includes Fortran programs.
External Links:: Document, ZentralBlatt
Referenced by:: §25.18(i), §25.21(iii).
Encodings:: BibTeX

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M. H. Halley, D. Delande, and K. T. Taylor (1993) The combination of

R

-matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr. J. Phys. B 26 (12), pp. 1775–1790.

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External Links:: ISSN 0953-4075, Document, MathReview
Referenced by:: 4th item.
Encodings:: BibTeX

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C. B. Haselgrove and J. C. P. Miller (1960) Tables of the Riemann Zeta Function. Royal Society Mathematical Tables, Vol. 6, Cambridge University Press, New York.

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External Links:: MathReview (D. H. Lehmer), ZentralBlatt
Referenced by:: §25.18(i), §25.18(ii).
Encodings:: BibTeX

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E. J. Heller, W. P. Reinhardt, and H. A. Yamani (1973) On an “equivalent quadrature” calculation of matrix elements of

(z-p^{2}/2m)^{-1}

using an

L^{2}

expansion technique. J. Comput. Phys. 13, pp. 536–550.

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External Links:: Document, Link
Referenced by:: §18.39(iv).
Encodings:: BibTeX

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C. S. Herz (1955) Bessel functions of matrix argument. Ann. of Math. (2) 61 (3), pp. 474–523.

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External Links:: FullText, MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: §35.1, §35.2, §35.3(ii), §35.5(i), §35.5(ii), §35.5(iii), §35.6(i), §35.6(ii), §35.6(iii), §35.6(iv), §35.7(i), §35.7(ii), §35.7(iv), §35.8(i), §35.8(ii), §35.8(iv), Ch.35, Notations P.
Encodings:: BibTeX

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T. H. Hildebrandt (1938) Definitions of Stieltjes Integrals of the Riemann Type. Amer. Math. Monthly 45 (5), pp. 265–278.

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External Links:: ISSN 0002-9890, Document, Link, MathReview Entry
Referenced by:: §1.16(ix).
Encodings:: BibTeX

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A. D. Alhaidari, E. J. Heller, H. A. Yamani, and M. S. Abdelmonem (Eds.) (2008) The

J

-Matrix Method. Developments and Applications. Springer-Verlag.

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External Links:: ISBN 978-1-4020-6072-4
Referenced by:: §18.39(iv).
Encodings:: BibTeX

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G. Allasia and R. Besenghi (1989) Numerical Calculation of the Riemann Zeta Function and Generalizations by Means of the Trapezoidal Rule. In Numerical and Applied Mathematics, Part II (Paris, 1988), C. Brezinski (Ed.), IMACS Ann. Comput. Appl. Math., Vol. 1, pp. 467–472.

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External Links:: MathReview
Referenced by:: §25.18(i).
Encodings:: BibTeX

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T. M. Apostol and T. H. Vu (1984) Dirichlet series related to the Riemann zeta function. J. Number Theory 19 (1), pp. 85–102.

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External Links:: ISSN 0022-314X, Document, MathReview (Kai Man Tsang), ZentralBlatt
Referenced by:: (25.16.10), (25.16.11), (25.16.12), (25.16.14), (25.16.15), (25.16.5), (25.16.6), (25.16.7), (25.16.8), (25.16.9), §25.16(ii), §25.16(ii), §25.16.
Encodings:: BibTeX

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T. M. Apostol (1985a) Formulas for higher derivatives of the Riemann zeta function. Math. Comp. 44 (169), pp. 223–232.

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External Links:: ISSN 0025-5718, FullText, MathReview (Aleksandar Ivić), ZentralBlatt
Referenced by:: (25.11.19), (25.11.20), (25.11.6), §25.11(vi), §25.18(i), (25.4.5), (25.4.6), §25.4, (25.6.11), (25.6.12), (25.6.13), (25.6.14), §25.6(ii), §25.6.
Encodings:: BibTeX

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J. V. Armitage (1989) The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System. In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.), London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.

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External Links:: MathReview, ZentralBlatt
Referenced by:: §25.17.
Encodings:: BibTeX

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Riemann matrix

11—20 of 25 matching pages

11: Bibliography B

12: 18.38 Mathematical Applications

Random Matrix Theory

Riemann–Hilbert Problems

13: Bibliography R

14: Bibliography C

15: 15.17 Mathematical Applications

16: Bibliography D

17: Software Index

18: Bibliography Y

19: Bibliography H

20: Bibliography