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1: 25.10 Zeros
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►More than 41% of all the zeros in the critical strip lie on the critical line (Bui et al. (2011)).
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2: Bibliography B
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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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3: Errata
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Subsection 25.10(ii)
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►These enable insertions of new numbered objects between existing ones without affecting their permanent identifiers and URLs.
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Equation (8.18.3)
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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).
8.18.3
The range of was extended to include . Previously this equation appeared without the order estimate as .
Reported 2016-08-30 by Xinrong Ma.
4: Viewing DLMF Interactive 3D Graphics
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►WebGL is a JavaScript API (application programming interface) for rendering 3D graphics in a web browser without the use of a plugin.
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5: Foreword
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►This could not have been done without the cooperation of many mathematicians, information technologists, and physical scientists both within NIST and externally.
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6: 27.15 Chinese Remainder Theorem
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►Even though the lengthy calculation is repeated four times, once for each modulus, most of it only uses five-digit integers and is accomplished quickly without overwhelming the machine’s memory.
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7: 18.30 Associated OP’s
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►The lowest order monic versions of both of these appear in §18.2(x), (18.2.31) defining the associated monic polynomials, and (18.2.32) their closely related cousins the corecursive polynomials.
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8: 15.13 Zeros
9: 19.15 Advantages of Symmetry
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►These reduction theorems, unknown in the Legendre theory, allow symbolic integration without imposing conditions on the parameters and the limits of integration (see §19.29(ii)).
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