The distribution of prime ideals of imaginary quadratic fields

Authors:
G. Harman, A. Kumchev and P. A. Lewis

Journal:
Trans. Amer. Math. Soc. **356** (2004), 599-620

MSC (2000):
Primary 11R44; Secondary 11N32, 11N36, 11N42.

Published electronically:
September 22, 2003

MathSciNet review:
2022713

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a primitive positive definite quadratic form with integer coefficients. Then, for all there exist such that is prime and

This is deduced from another result giving an estimate for the number of prime ideals in an ideal class of an imaginary quadratic number field that fall in a given sector and whose norm lies in a short interval.

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Additional Information

**G. Harman**

Affiliation:
Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom

Email:
G.Harman@rhul.ac.uk

**A. Kumchev**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3

Email:
kumchev@math.toronto.edu

**P. A. Lewis**

Affiliation:
School of Mathematics, Cardiff University, P.O. Box 926, Cardiff CF24 4YH, Wales, United Kingdom

Email:
LewisPA3@Cardiff.ac.uk

DOI:
http://dx.doi.org/10.1090/S0002-9947-03-03104-0

Received by editor(s):
January 11, 2002

Received by editor(s) in revised form:
April 22, 2002

Published electronically:
September 22, 2003

Additional Notes:
The second author was partially supported by NSF Grant DMS 9970455 and NSERC Grant A5123.

The third author was supported by an EPSRC Research Studentship.

Article copyright:
© Copyright 2003
American Mathematical Society