additive number theory

SearchAdvancedHelp

(0.002 seconds)

5 matching pages

1: 27.1 Special Notation

§27.1 Special Notation

… ► ►►

$d,k,m,n$	positive integers (unless otherwise indicated).
…

2: 27.13 Functions

… ►

§27.13(i) Introduction

… ►The subsections that follow describe problems from additive number theory. … ►

§27.13(ii) Goldbach Conjecture

… ►

§27.13(iii) Waring’s Problem

… ►

§27.13(iv) Representation by Squares

…

3: 27.14 Unrestricted Partitions

… ►Euler’s pentagonal number theorem states that … ►

§27.14(iv) Relation to Modular Functions

… ►

§27.14(v) Divisibility Properties

… ►

§27.14(vi) Ramanujan’s Tau Function

… ►

4: 27.22 Software

… ►In this section we provide links to the known sources of software for factorization and primality testing, as well as additional Web-based resources for information on these topics. … ►

Mathematica. PrimeQ combines strong pseudoprime tests for the bases 2 and 3 and a Lucas pseudoprime test. No known composite numbers pass these three tests, and Bleichenbacher (1996) has shown that this combination of tests proves primality for integers below ${10}^{16}$. Provable PrimeQ uses the Atkin–Goldwasser–Kilian–Morain Elliptic Curve Method to prove primality. FactorInteger tries Brent–Pollard rho, Pollard $p-1$, and then cfrac after trial division. See §27.19. ecm is available also, and the Multiple Polynomial Quadratic sieve is expected in a future release.

For additional Mathematica routines for factorization and primality testing, including several different pseudoprime tests, see Bressoud and Wagon (2000).

… ►

Number Theory Web. References and links to software for factorization and primality testing.

…

5: Bibliography V

… ►

Some Wonderful Formulas $\mathrm{\dots }$ an Introduction to Polylogarithms. In Proceedings of the Queen’s Number Theory Conference, 1979 (Kingston, Ont., 1979), R. Ribenboim (Ed.), Queen’s Papers in Pure and Appl. Math., Vol. 54, Kingston, Ont., pp. 269–286.

ⓘ

External Links:

MathReview (F. Beukers), ZentralBlatt

Referenced by:

(25.6.10), (25.6.8), (25.6.9), §25.6(i), §25.6.

Encodings:

BibTeX

… ►

Integrating products of Bessel functions with an additional exponential or rational factor. Comput. Phys. Comm. 178 (8), pp. 578–590.

ⓘ

Notes:

Associated computer program available online

External Links:

ISSN 0010-4655, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§10.74(vii), §10.74(vii).

Encodings:

BibTeX

… ►

Quantum Theory of Angular Momentum. World Scientific Publishing Co. Inc., Singapore.

ⓘ

External Links:

ISBN 9971-50-107-4, MathReview (M. A. Rashid), ZentralBlatt

Referenced by:

§16.24(iii), §34.1, §34.11, §34.13, §34.13, §34.14, §34.2, §34.3(iii), §34.3(vi), §34.4, §34.4, §34.5(iii), §34.5(vi), §34.7(ii), §34.7(iii), §34.8, §34.9, Ch.34.

Encodings:

BibTeX

… ►

Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, RI.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§13.27.

Encodings:

BibTeX

… ►

The topological degree theory for the localization and computation of complex zeros of Bessel functions. Numer. Funct. Anal. Optim. 18 (1-2), pp. 227–234.

ⓘ

External Links:

ISSN 0163-0563, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

Encodings:

BibTeX