Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T05:50:14.389Z Has data issue: false hasContentIssue false

THE DISTRIBUTION OF $k$ -TUPLES OF REDUCED RESIDUES

Published online by Cambridge University Press:  13 August 2014

Farzad Aryan*
Affiliation:
Department of Mathematics and Computer Science, University of Lethbridge, C526 University Hall, 4401 University Drive, Lethbridge T1K 3M4, Canada email [email protected]
Get access

Abstract

In 1940 Paul Erdős made a conjecture about the distribution of reduced residues. Here we study the distribution of $k$-tuples of reduced residues.

MSC classification

Type
Research Article
Copyright
Copyright © University College London 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cramer, H., On the order of magnitude of the difference between consecutive prime numbers. Acta Arith. 2 1936, 2346.Google Scholar
Granville, A., Harold Cramer and the distribution of prime numbers. Scand. Actuar. J. 1 1995, 1228.Google Scholar
Erdős, P., The difference of consecutive primes. Duke Math. J. 6 1940, 438441.Google Scholar
Hooley, C., On the difference of consecutive numbers prime to n. Acta Arith. 8 1962/1963, 343347.CrossRefGoogle Scholar
Hausman, M. and Shapiro, H., On the mean square distribution of primitive roots of unity. Comm. Pure Appl. Math. 26 1973, 539547.Google Scholar
Montgomery, H. and Vaughan, R., On the distribution of reduced residues. Ann. of Math. (2) 123(2) 1986, 311333.CrossRefGoogle Scholar
Halberstam, H. and Richert, H. E., Sieve Methods (London Mathematical Society Monographs 4), Academic Press (London, New York, 1974).Google Scholar
Montgomery, H. L. and Soundararajan, K., Primes in short intervals. Comm. Math. Phys. 252(1–3) 2004, 589617.Google Scholar