number-theoretic%20functions

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1: 6.16 Mathematical Applications

… ►It occurs with Fourier-series expansions of all piecewise continuous functions. … … ►

§6.16(ii) Number-Theoretic Significance of $\mathrm{li}\left(x\right)$

►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 …where $\pi (x)$ is the number of primes less than or equal to $x$. …

2: 27.2 Functions

… ►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes. …There is great interest in the function $\pi \left(x\right)$ that counts the number of primes not exceeding $x$. … ►Other examples of number-theoretic functions treated in this chapter are as follows. … ► …is the number of divisors of $n$ and is the divisor function. …

3: Bibliography M

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Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Australia.

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Notes:

A software package (the successor to CAYLEY) designed to solve computationally hard problems in algebra, number theory, geometry, and combinatorics, and to provide a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric, and geometric objects.

External Links:

Magma

Referenced by:

4th item.

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Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

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External Links:

ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(iii).

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BibTeX

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Methods of Theoretical Physics. Vol. 1, McGraw-Hill Book Co., New York.

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Notes:

Reprinted by Feshbach Publishing, http://www.feshbachpublishing.com/.

External Links:

Feshbach Publishing, MathReview (M. Pinl), ZentralBlatt

Referenced by:

§1.17(iii), §1.5(ii), §12.17, §12.17, §12.17.

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Methods of Theoretical Physics. Vol. 2, McGraw-Hill Book Co., New York.

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Notes:

Reprinted by Feshbach Publishing, http://www.feshbachpublishing.com/.

External Links:

Feshbach Publishing, MathReview (M. Pinl), ZentralBlatt

Referenced by:

§12.17, §12.17.

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Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 211, pp. 33–47.

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External Links:

MathReview (J. Meixner), ZentralBlatt

Referenced by:

§30.9(ii), §30.9(ii).

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