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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 11K: Probabilistic theory: distribution modulo 1; metric theory of algorithms

Introduction

History

Applications and related fields

Subfields

• 11K06: General theory of distribution modulo 1 [See also 11J71]
• 11K16: Normal numbers, radix expansions, etc. [See also 11A63]
• 11K31: Special sequences
• 11K36: Well-distributed sequences and other variations
• 11K38: Irregularities of distribution, discrepancy [See also 11Nxx]
• 11K41: Continuous, p-adic and abstract analogues
• 11K45: Pseudo-random numbers; Monte Carlo methods
• 11K50: Metric theory of continued fractions [See also 11A55, 11J70]
• 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
• 11K60: Diophantine approximation [See also 11Jxx]
• 11K65: Arithmetic functions [See also 11Nxx]
• 11K70: Harmonic analysis and almost periodicity
• 11K99: None of the above, but in this section

Parent field: 11: Number Theory

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

• Elliott, Peter D. T. A.: "Probabilistic number theory", Grundlehren der Mathematischen Wissenschaften 240, Springer-Verlag, Berlin-New York, 1980. 341 pp. ISBN 0-387-90438-7
• Tenenbaum, Gérald, "Introduction to analytic and probabilistic number theory", Cambridge University Press, Cambridge, 1995. 448 pp. ISBN 0-521-41261-7
• Montgomery, Hugh L.: "Ten lectures on the interface between analytic number theory and harmonic analysis", American Mathematical Society, Providence, RI, 1994.220 pp. ISBN 0-8218-0737-4
• Deshouillers, Jean-Marc; Tenenbaum, Gérald, "Survol de la théorie probabiliste des nombres et de quelques progrès récents", Progr. Math., 59, Birkhäuser Boston, Boston, Mass., 1985.

Software and tables

Other web sites with this focus

Selected topics at this site

• Seeking sum(int(ax+b), x=1..n)
• Fejer's theorem (sequences mod 1)
• Sequences such as {(n*alpha, n*beta)} are dense on the torus
• Is the sequence { n*sin(n) } dense in the real line?
• Van der Waerden's theorem: sufficiently large collections of integers must contain long arithmetic progressions
• Arithmetic progressions of square-free integers