Geodesic
The distribution of certain special values of the cubic Legendre symbol
Glasgow mathematical journal, Tome 26 (1985), pp. 165-184

Voir la notice de l'article provenant de la source Cambridge University Press

Let ω be a primitive cube root of unity. We define the cubic residue symbol (Legendre symbol) on Z[ω] as follows. Let πεZ[ω] be a prime, (3, π)=1. For α ε Z[ω] such that (α, π)=1 we let be that third root of unity so that 
Patterson, S. J. The distribution of certain special values of the cubic Legendre symbol. Glasgow mathematical journal, Tome 26 (1985), pp. 165-184. doi: 10.1017/S0017089500006169
@article{10_1017_S0017089500006169,
     author = {Patterson, S. J.},
     title = {The distribution of certain special values of the cubic {Legendre} symbol},
     journal = {Glasgow mathematical journal},
     pages = {165--184},
     year = {1985},
     volume = {26},
     doi = {10.1017/S0017089500006169},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006169/}
}
TY  - JOUR
AU  - Patterson, S. J.
TI  - The distribution of certain special values of the cubic Legendre symbol
JO  - Glasgow mathematical journal
PY  - 1985
SP  - 165
EP  - 184
VL  - 26
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006169/
DO  - 10.1017/S0017089500006169
ID  - 10_1017_S0017089500006169
ER  - 
%0 Journal Article
%A Patterson, S. J.
%T The distribution of certain special values of the cubic Legendre symbol
%J Glasgow mathematical journal
%D 1985
%P 165-184
%V 26
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006169/
%R 10.1017/S0017089500006169
%F 10_1017_S0017089500006169

[1] 1.Bass, H., Milnor, J. and Serre, J-P, Solution of the congruence subgroup problem for SL(n≥3) and Sp(n≥2). Publ. Math. I.H.E.S. 33 (1967), 59–137. Google Scholar | DOI

[2] 2.Elstrodt, J., Grunewald, E. and Mennicke, J., Discontinuous groups on three-dimensional hyperbolic space; analytic theory and number-theory applications, work in progress. Google Scholar

[3] 3.Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (O.U.P., 1960). Google Scholar

[4] 4.Heath-Brown, D. R. and Patterson, S. J., On the distribution of cubic Gauss sums at prime arguments, J. Reine Angew. Math. 310 (1979), 111–130. Google Scholar

[5] 5.Kazhdan, D. A. and Patterson, S. J., Metaplectic forms, Publ. Math. I.H.E.S., 59 (1984), 35–142. Google Scholar | DOI

[6] 6.Lang, S., Algebraic number theory (Addison-Wesley, 1970). Google Scholar

[7] 7.Matthews, C. R., Gauss sums and elliptic functions, II. The quartic case, Invent. Math. 54 (1979), 23–52. Google Scholar

[8] 8.Neuenhöffer, H., Über die analytische Fortsetzung von Poincaréreihen, S.B. Heidelberger Akad. Wiss. Math.-Nat. Kl. (1973), 33–90. Google Scholar

[9] 9.Ogg, A., Modular forms and Dirichlet series (Benjamin, 1969). Google Scholar

[10] 10.Patterson, S. J., A cubic analogue of the theta series, J. Reine Angew. Math. 296 (1977), 125–161, 217–220. Google Scholar

[11] 11.Patterson, S. J., The distribution of general Gauss sums at prime arguments, in Halberstam, H. and Hooley, C., ed., Recent progress in analytic number theory, Vol. 2 (Academic Press, 1981). Google Scholar

[12] 12.Rademacher, H., Topics in analytic number theory (Springer, 1973). Google Scholar

[13] 13.Serre, J-P., A functorial property of power residue symbols, Publ. Math. I.H.E.S. 44 (1974), 241–244. Google Scholar

[14] 14.Titchmarsh, E. C., The theory of the Riemann zeta-function (O.U.P., 1951). Google Scholar

Cité par Sources :