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1: 34.10 Zeros

… ►Such zeros are called trivial zeros. …

2: 25.10 Zeros

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§25.10(i) Distribution

… ►These are called the trivial zeros. Except for the trivial zeros, $\zeta \left(s\right)\ne 0$ for $\mathrm{\Re }s\le 0$. …

3: 25.15 Dirichlet $L$-functions

… ►Since $L(s,\chi )\ne 0$ if $\mathrm{\Re }s>1$, (25.15.5) shows that for a primitive character $\chi$ the only zeros of $L(s,\chi )$ for (the so-called trivial zeros) are as follows: …

4: 24.16 Generalizations

… ►Let ${\chi }_0$ be the trivial character and ${\chi }_4$ the unique (nontrivial) character with $f=4$; that is, ${\chi }_4(1)=1$, ${\chi }_4(3)=-1$, ${\chi }_4(2)={\chi }_4(4)=0$. …

5: Bibliography

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Note on the trivial zeros of Dirichlet $L$-functions. Proc. Amer. Math. Soc. 94 (1), pp. 29–30.

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External Links:

ISSN 0002-9939, FullText, MathReview (Jerzy Kaczorowski), ZentralBlatt

Referenced by:

(25.15.7), (25.15.8), §25.15(ii), §25.15.

Encodings:

BibTeX

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6: 18.33 Polynomials Orthogonal on the Unit Circle

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Trivial

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7: 18.18 Sums

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