relation to zeros

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1: 25.17 Physical Applications

§25.17 Physical Applications

… ►This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian. …

2: 9.9 Zeros

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§9.9(ii) Relation to Modulus and Phase

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3: 25.10 Zeros

… ►Calculations relating to the zeros on the critical line make use of the real-valued function …

4: 7.13 Zeros

… ►In consequence of (7.5.5) and (7.5.10), zeros of $ℱ\left(z\right)$ are related to zeros of $\mathrm{erfc}z$. …

5: Bibliography L

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Monotonic sequences related to zeros of Bessel functions. Numer. Algorithms 49 (1-4), pp. 221–233.

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External Links:

ISSN 1017-1398, Document, FullText, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§10.21(iv), §10.21(iv).

Encodings:

BibTeX

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6: 10.21 Zeros

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${\varphi }_{\nu }\left(y_{\nu ,m}^{\prime }\right)=m\pi ,$ $m=1,2,\mathrm{\dots }$.

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7: 36.7 Zeros

… ►Outside the bifurcation set (36.4.10), each rib is flanked by a series of zero lines in the form of curly “antelope horns” related to the “outside” zeros (36.7.2) of the cusp canonical integral. …

8: Bibliography B

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Concerning the zeros of some functions related to Bessel functions. J. Mathematical Phys. 10 (9), pp. 1729–1744.

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External Links:

Document, MathReview (C. V. Coffman), ZentralBlatt

Referenced by:

§10.21(xi).

Encodings:

BibTeX

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9: 29.12 Definitions

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§29.12(i) Elliptic-Function Form

… ►There are eight types of Lamé polynomials, defined as follows: … ►The superscript $m$ on the left-hand sides of (29.12.1)–(29.12.8) agrees with the number of $z$-zeros of each Lamé polynomial in the interval $(0,K)$, while $n-m$ is the number of $z$-zeros in the open line segment from $K$ to $K+\mathrm{i}{K}^{\prime }$. … ►

§29.12(iii) Zeros

►Let ${\xi }_1,{\xi }_2,\mathrm{\dots },{\xi }_n$ denote the zeros of the polynomial $P$ in (29.12.9) arranged according to …

10: 6.16 Mathematical Applications

… ►If we assume Riemann’s hypothesis that all nonreal zeros of $\zeta \left(s\right)$ have real part of $\frac{1}{2}$ (§25.10(i)), then …