On the exact degree of over

Authors:
R. Balasubramanian, F. Luca and R. Thangadurai

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2283-2288

MSC (2010):
Primary 11A15

Published electronically:
March 15, 2010

MathSciNet review:
2607857

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite set of non-zero integers. In this paper, we give an exact formula for the degree of the multi-quadratic field over . To do this, we compute the relative density of the set of prime numbers for which all the 's are simultaneously quadratic residues modulo in two ways.

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Additional Information

**R. Balasubramanian**

Affiliation:
Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India

Email:
balu@imsc.res.in

**F. Luca**

Affiliation:
Mathematical Institute, Universidad Nacional Autónoma de México, Ap. Postal, 61-3 (Xangari), CP 58089, Morelia, Michoacán, Mexico

Email:
fluca@matmor.unam.mx

**R. Thangadurai**

Affiliation:
Department of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India

Email:
thanga@hri.res.in

DOI:
http://dx.doi.org/10.1090/S0002-9939-10-10331-1

Keywords:
Quadratic residues,
Galois field,
Chebotarev density theorem

Received by editor(s):
September 15, 2009

Published electronically:
March 15, 2010

Communicated by:
Ken Ono

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.