Divisors

Richard R. Hall, Gérald Tenenbaum (Autoren)

Buch | Softcover

184 Seiten

2008
Cambridge University Press (Verlag)
978-0-521-09167-1 (ISBN)

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This is a systematic account of the multiplicative structure of integers, from the probabilistic point of view. The authors are especially concerned with the distribution of the divisors, which is as fundamental and important as the additive structure of the integers, and yet until now has hardly been discussed outside of the research literature. Hardy and Ramanujan initiated this area of research and it was developed by Erdös in the thirties. His work led to some deep and basic conjectures of wide application which have now essentially been settled. This book contains detailed proofs, some of which have never appeared in print before, of those conjectures that are concerned with the propinquity of divisors. Consequently it will be essential reading for all researchers in analytic number theory.

1. Preliminaries; 2. The Normal Distribution of the Prime Factors; 3. Sieving by an Interval; 4. Imaginary Powers; 5. Measures of Propinquity; 6. Erdös' Conjecture; 7. Hooley's Δr-functions - Sharp Bounds; 8. Hooley's Δr-functions - the Critical Interval.

Erscheint lt. Verlag	4.12.2008
Reihe/Serie	Cambridge Tracts in Mathematics
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	280 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	0-521-09167-5 / 0521091675
ISBN-13	978-0-521-09167-1 / 9780521091671
Zustand	Neuware