×

Sommes de carres et d’irreductibles dans F//q[X]. (French) Zbl 0493.12021


MSC:

11T06 Polynomials over finite fields
11P05 Waring’s problem and variants
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML

References:

[1] R. Ayoub . An introduction to the analytic theory of numbers . Mathematical Surveys n^\circ 10 , Amer. Math. Soc. MR 160743 | Zbl 0128.04303 · Zbl 0128.04303
[2] M. Car . Le problème de Waring pour l’anneau des polynômes sur un corps fini . C.R.A.S. , Paris , Série A et B , 273 , ( 1971 ). MR 282937 | Zbl 0221.10060 · Zbl 0221.10060
[3] L. Carlitz . On the representations of a polynomial on a Galois field as the sum of an even number of squares . Trans. Amer. Math. Soc. , 35 , ( 1933 ), pp. 397 - 410 . MR 1501692 | Zbl 0006.38901 · Zbl 0006.38901
[4] L. Carlitz . On the representations of a polynomial on a Galois field as the sum of an odd number of squares . Duke Math. Jour. , 1 , ( 1935 ), pp. 298 - 315 . Article | Zbl 0012.19305 | JFM 61.0126.02 · Zbl 0012.19305
[5] L. Carlitz . Sums of squares of polynomials . Duke Math Jour. , 3 , ( 1937 ), pp. 1 - 7 . Article | MR 607 | Zbl 0016.14802 | JFM 63.0104.01 · Zbl 0016.14802
[6] L. Carlitz . The singular series for sums of squares of polynomials Duke Math. Jour. , 14 , ( 1947 ), pp. 1105 - 1120 . Article | MR 23304 | Zbl 0032.00204 · Zbl 0032.00204
[7] L. Carlitz . A note on sums of three squares in GF [q,x] . Mathematics Magazine , 48 , ( 1975 ), pp. 109 - 110 . MR 360539 | Zbl 0313.10046 · Zbl 0313.10046
[8] Eckford-Cohen . Sums of an even numbers of squares in GF[pn,x] , I . Duke Math. Jour. , 14 , ( 1947 ), pp. 251 - 267 . Article | MR 21571 | Zbl 0030.10401 · Zbl 0030.10401
[9] Eckford-Cohen . Sums of an even number of squares in GF[pn,x] , II . Duke Math. Jour. , 14 , ( 1947 ), pp. 543 - 557 . Article | MR 22233 | Zbl 0030.10402 · Zbl 0030.10402
[10] Ellison & Mendes-France . Les nombres premiers . Hermann , Paris . · Zbl 0313.10001
[11] D.R. Hayes . The expression of a polynomial as the sum of three irreducibles . Acta. Arith. , 11 , ( 1966 ), pp. 461 - 488 . Article | MR 201422 | Zbl 0151.03902 · Zbl 0151.03902
[12] K. Prachar . Primzahlverteilung . Springer-Verlag , Berlin . · Zbl 0080.25901
[13] G. Rhin . Répartition modulo 1 dans un corps de séries formelles sur un corps fini . Thèse soutenue à l’Université de Paris VI , ( 1971 ). MR 349612 | Zbl 0252.10036 · Zbl 0252.10036
[14] G. Rhin . Répartition modulo 1 dans un corps de séries formelles sur un corps fini . Dissertationes mathematicae , ( 1972 ). MR 349612 | Zbl 0252.10036 · Zbl 0252.10036
[15] W. Webb . Waring’s problem in GF[q,x] . Acta. Arith. , 22 , ( 1972 ), pp. 207 - 220 . Article | MR 313190 | Zbl 0258.12014 · Zbl 0258.12014
[16] W. Webb . On the representation of polynomials over finite fields as sums of powers and irreducibles . Rocky Mountain J. Math. , 3 , ( 1973 ), pp. 23 - 29 . MR 347784 | Zbl 0258.10028 · Zbl 0258.10028
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.