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1: 25.10 Zeros

… ►More than 41% of all the zeros in the critical strip lie on the critical line (Bui et al. (2011)). …

2: Bibliography B

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Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces. J. Phys. A 8 (4), pp. 566–584.

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External Links:

Document, MathReview

Referenced by:

§36.14(iii).

Encodings:

BibTeX

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More than 41% of the zeros of the zeta function are on the critical line. Acta Arith. 150 (1), pp. 35–64.

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External Links:

ISSN 0065-1036, Document, Link, MathReview (Timothy S. Trudgian), ZentralBlatt

Referenced by:

§25.10(ii), §25.10(ii), Erratum (V1.1.4) for Subsection 25.10(ii).

Encodings:

BibTeX

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3: Daniel W. Lozier

… ►In 1963–1969 he worked at the U. …Army Engineer Research and Development Laboratory in Virginia on finite-difference solutions of differential equations associated with nuclear weapons effects. …

4: Errata

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In the paragraph immediately below (25.10.4), it was originally stated that “more than one-third of all zeros in the critical strip lie on the critical line.” which referred to Levinson (1974). This sentence has been updated with “one-third” being replaced with “41%” now referring to Bui et al. (2011) (suggested by Gergő Nemes on 2021-08-23).

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Factors inside square roots on the right-hand sides of formulas (19.18.6), (19.20.10), (19.20.19), (19.21.7), (19.21.8), (19.21.10), (19.25.7), (19.25.10) and (19.25.11) were written as products to ensure the correct multivalued behavior.

Reported by Luc Maisonobe on 2021-06-07

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A note about the multivalued nature of the Kummer confluent hypergeometric function of the second kind $U$ on the right-hand side of (7.18.10) was inserted.

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The factor on the right-hand side containing $\cos (\mu -\nu )\theta$ has been been replaced with $\cos \left((\mu -\nu )\theta \right)$ to clarify the meaning.

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Originally was expressed in term of asymptotic symbol $\sim$. As a consequence of the use of the $O$ order symbol on the right-hand side, $\sim$ was replaced by $=$.

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5: 7.21 Physical Applications

… ►Ng and Geller (1969) cites work with applications from atomic physics and astrophysics. … ►Voigt functions $𝖴(x,t)$, $𝖵(x,t)$, can be regarded as the convolution of a Gaussian and a Lorentzian, and appear when the analysis of light (or particulate) absorption (or emission) involves thermal motion effects. …Dawson’s integral appears in de-convolving even more complex motional effects; see Pratt (2007). …

6: Foreword

… ►That 1046-page tome proved to be an invaluable reference for the many scientists and engineers who use the special functions of applied mathematics in their day-to-day work, so much so that it became the most widely distributed and most highly cited NIST publication in the first 100 years of the institution’s existence. … ►The DLMF may well serve as a model for the effective presentation of highly mathematical reference material on the Web. …

7: About MathML

… ►In rare cases, a browser lacks both MathML support and a robust enough javascript implementation capable of running MathJax; you may wish to visit the Customize DLMF page and choose the HTML+images document format. … ►Most modern browsers support ‘Web Fonts’, fonts that are effectively included with a web site. …

8: Philip J. Davis

… ►During World War II he worked on problems in aerodynamics for the National Advisory Committee for Aeronautics (NACA) at Langley Airforce Base in Hampton, VA. … ►After being asked by Milton Abramowitz to work on the project, he chose to write the Chapter “Gamma Function and Related Functions. … ►NBS mathematician Irene Stegun took over management of the A&S project which was already well on its way, and led the work to publication in 1964. … ►This immediately led to discussions among some of the project members about what might be possible, and the discovery that some interactive graphics work had already been done for the NIST Matrix Market, a publicly available repository of test matrices for comparing the effectiveness of numerical linear algebra algorithms. …

9: Tom M. Apostol

… ►He was a visiting professor at the University of Patras in Greece in 1978, and was elected a Corresponding Member of the Academy of Athens in 2001 (where he delivered his inaugural lecture in Greek). ►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. … ►He additionally served as a visiting lecturer for the MAA, and as a member of the MAA Board of Governors. …

10: 25.17 Physical Applications

… ►See Armitage (1989), Berry and Keating (1998, 1999), Keating (1993, 1999), and Sarnak (1999). … ►Quantum field theory often encounters formally divergent sums that need to be evaluated by a process of regularization: for example, the energy of the electromagnetic vacuum in a confined space (Casimir–Polder effect). …