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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: Stephen M. Watt

… ►Prior to joining the University of Waterloo, Watt was Distinguished University Professor of the University of Western Ontario and Professor at the University of Nice-Sophia Antipolis. …

3: Bibliography B

… ►

H. M. Bui, B. Conrey, and M. P. Young (2011) More than 41% of the zeros of the zeta function are on the critical line. Acta Arith. 150 (1), pp. 35–64.

ⓘ

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

…

4: 34.14 Tables

… ►Biedenharn and Louck (1981) give tables of algebraic expressions for Clebsch–Gordan coefficients and

\mathit{6j}

symbols, together with a bibliography of tables produced prior to 1975. …

5: 13.30 Tables

… ►For other tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).

6: 18.41 Tables

… ►For tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).

7: Errata

… ►

Equations (32.8.10), (32.10.9)

32.8.10

\tau_{n}(z)=\mathscr{W}\left\{p_{1}(z),p_{3}(z),\ldots,p_{2n-1}(z)\right\}

32.10.9

\tau_{n}(z)=\mathscr{W}\left\{\phi(z),\phi^{\prime}(z),\ldots,\phi^{(n-1)}(z)\right\}

The right-hand side of these equation, which was originally written as a matrix determinant, was rewritten using the Wronskian determinant notation. Also, in each preceding sentence, the word ‘determinant’ was replaced with ‘Wronskian determinant’.

… ►

Subsection 25.10(ii)

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).

… ►

Subsections 10.6(i), 10.29(i)

Sentences were added just below (10.6.5) and (10.29.3) regarding results on modified quotients of the form $\ifrac{z\mathscr{C}_{\nu\pm 1}\left(z\right)}{\mathscr{C}_{\nu}\left(z\right)}$ and $\ifrac{z\mathscr{Z}_{\nu\pm 1}\left(z\right)}{\mathscr{Z}_{\nu}\left(z\right)}$ , respectively (suggested by Art Ballato on 2021-04-29).

… ►

Section 1.14

There have been extensive changes in the notation used for the integral transforms defined in §1.14. These changes are applied throughout the DLMF. The following table summarizes the changes.

Transform	New	Abbreviated	Old
	Notation	Notation	Notation
Fourier	$\mathscr{F}\left(f\right)\left(x\right)$	$\mathscr{F}\mskip-3.0muf\mskip 3.0mu\left(x\right)$
Fourier Cosine	$\mathscr{F}_{\mkern-3.0muc}\left(f\right)\left(x\right)$	$\mathscr{F}_{\mkern-3.0muc}\mskip-1.0muf\mskip 3.0mu\left(x\right)$
Fourier Sine	$\mathscr{F}_{\mkern-2.0mus}\left(f\right)\left(x\right)$	$\mathscr{F}_{\mkern-2.0mus}\mskip-1.0muf\mskip 3.0mu\left(x\right)$
Laplace	$\mathscr{L}\left(f\right)\left(s\right)$	$\mathscr{L}\mskip-3.0muf\mskip 3.0mu\left(s\right)$	$\mathscr{L}(f(t);s)$
Mellin	$\mathscr{M}\left(f\right)\left(s\right)$	$\mathscr{M}\mskip-3.0muf\mskip 3.0mu\left(s\right)$	$\mathscr{M}(f;s)$
Hilbert	$\mathcal{H}\left(f\right)\left(s\right)$	$\mathcal{H}\mskip-3.0muf\mskip 3.0mu\left(s\right)$	$\mathcal{H}(f;s)$
Stieltjes	$\mathcal{S}\left(f\right)\left(s\right)$	$\mathcal{S}\mskip-3.0muf\mskip 3.0mu\left(s\right)$	$\mathcal{S}(f;s)$

Previously, for the Fourier, Fourier cosine and Fourier sine transforms, either temporary local notations were used or the Fourier integrals were written out explicitly.

… ►

Equation (10.17.14)

10.17.14

\left|R_{\ell}^{\pm}(\nu,z)\right|\leq 2|a_{\ell}(\nu)|\mathcal{V}_{z,\pm% \mathrm{i}\infty}\left(t^{-\ell}\right)\*\exp\left(|\nu^{2}-\tfrac{1}{4}|% \mathcal{V}_{z,\pm\mathrm{i}\infty}\left(t^{-1}\right)\right)

Originally the factor $\mathcal{V}_{z,\pm\mathrm{i}\infty}\left(t^{-1}\right)$ in the argument to the exponential was written incorrectly as $\mathcal{V}_{z,\pm\mathrm{i}\infty}\left(t^{-\ell}\right)$ .

Reported 2014-09-27 by Gergő Nemes.

…

8: 22.21 Tables

… ►For other tables prior to 1961 see Fletcher et al. (1962, pp. 500–503) and Lebedev and Fedorova (1960, pp. 221–223). …

9: 27.21 Tables

… ►Those published prior to 1918 are mentioned in Dickson (1919). …

10: 12.19 Tables

… ►For other tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).