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Car, Mireille

Sommes de carrés et d’irréductibles dans \(\mathbb F_q[X]\). (French) Zbl 0493.12021

Ann. Fac. Sci. Toulouse, V. Sér., Math. 3, 129-166 (1981).
Reviewer: Mireille Car (Marseille)
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0493.12021

Cited in 1 Review
Cited in 2 Documents

MSC:

11T06 Polynomials over finite fields
11P05 Waring’s problem and variants

Keywords:

circle method; polynomials; finite field
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Full Text: DOI Numdam EuDML

References:

[1] Ayoub, R.. «An introduction to the analytic theory of numbers». Mathematical Surveys n° 10, Amer. Math. Soc. · Zbl 0128.04303
[2] Car, M.. «Le problème de Waring pour l’anneau des polynômes sur un corps fini». C.R.A.S., Paris, Série A et B, 273, (1971). · Zbl 0221.10060
[3] Carlitz, L.. «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. · Zbl 0006.38901
[4] Carlitz, L.. «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. · JFM 61.0126.02
[5] Carlitz, L.. «Sums of squares of polynomials». Duke Math Jour., 3, (1937), pp. 1-7. · JFM 63.0104.01
[6] Carlitz, L.. «The singular series for sums of squares of polynomials»Duke Math. Jour., 14, (1947), pp. 1105-1120. · Zbl 0032.00204
[7] Carlitz, L.. «A note on sums of three squares in GF [q,x] ». Mathematics Magazine, 48, (1975), pp. 109-110. · 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. · 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. · Zbl 0030.10402
[10] Ellison & Mendes-France. «Les nombres premiers». Hermann, Paris. · Zbl 0313.10001
[11] Hayes, D.R.. «The expression of a polynomial as the sum of three irreducibles». Acta. Arith., 11, (1966), pp. 461-488. · Zbl 0151.03902
[12] Prachar, K.. «Primzahlverteilung». Springer-Verlag, Berlin.
[13] Rhin, G.. «Répartition modulo 1 dans un corps de séries formelles sur un corps fini». Thèse soutenue à l’Université de Paris VI, (1971 ). · Zbl 0252.10036
[14] Rhin, G.. « Répartition modulo 1 dans un corps de séries formelles sur un corps fini». Dissertationes mathematicae, (1972). · Zbl 0252.10036
[15] Webb, W.. «Waring’s problem in GF[q,x] ». Acta. Arith., 22, (1972), pp. 207-220. · Zbl 0258.12014
[16] Webb, W.. «On the representation of polynomials over finite fields as sums of powers and irreducibles». Rocky Mountain J. Math., 3, (1973), pp. 23-29. · Zbl 0258.10028
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