Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T22:56:08.354Z Has data issue: false hasContentIssue false
  • English
  • Français

A quadratic large sieve inequality over number fields

Published online by Cambridge University Press:  03 October 2012

LEO GOLDMAKHER  and
BENOÎT LOUVEL
LEO GOLDMAKHER
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, Canada. e-mail: leo.goldmakher@utoronto.ca
BENOÎT LOUVEL
Affiliation:
Mathematisches Institut Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany. e-mail: blouvel@uni-math.gwdg.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We formulate and prove a large sieve inequality for quadratic characters over a number field. To do this, we introduce the notion of an n-th order Hecke family. We develop the basic theory of these Hecke families, including versions of the Poisson summation formula.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 2 , March 2013 , pp. 193 - 212
Copyright
Copyright © Cambridge Philosophical Society 2012

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

REFERENCES

[BGL]Blomer, V., Goldmakher, L. and Louvel, B.L-functions with n-th order twists, preprint.Google Scholar
[CF]Cassels, J. W. S. and Fröhlich, A. (eds.), Algebraic Number Theory (Academic Press, 1967).Google Scholar
[FF]Fisher, B. and Friedberg, S.Double Dirichlet series over function fields. Compos. Math. 140 (2003), 613–630.CrossRefGoogle Scholar
[FHL]Friedberg, S., Hoffstein, J. and Lieman, D.Double Dirichlet series and the n-th order twists of Hecke L-series. Math. Ann. 327 (2003), 315–338.CrossRefGoogle Scholar
[Ha]Hasse, H.Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Teil II: Reziprozitätsgesetz (Physica-Verlag, Würzburg 1965).CrossRefGoogle Scholar
[HB]Heath–Brown, D. R.A mean value estimate for real character sums. Acta Arith. 72 (1995), 237–275.CrossRefGoogle Scholar
[HB2]Heath–Brown, D. R.Kummer's conjecture for cubic Gauss sums. Israel J. Math. 120 part A (2000), 97–124.CrossRefGoogle Scholar
[HBP]Heath–Brown, D. R. and Patterson, S. J.The distribution of Kummer sums at prime arguments. J. Reine Angew. Math. 310 (1979), 111–130.Google Scholar
[Mo]Montgomery, H. L.The analytic principle of the large sieve. Bull. AMS 84, No. 4 (1978), 547–567.CrossRefGoogle Scholar
[On]Onodera, K.Bound for the sum involving the Jacobi symbol in. Funct. Approx. Comment. Math. 41 (2009), 71–103.CrossRefGoogle Scholar
[SD]Swinnerton–Dyer, H. P. F.A brief guide to algebraic number theory. London Math. Soc. Student Texts, Vol. 50 (Cambridge University Press, Cambridge 2001).CrossRefGoogle Scholar