Partitions quadratiques et cyclotomie
Séminaire Delange-Pisot-Poitou. Théorie des nombres, Volume 16 (1974-1975) no. 2, Talk no. G13, 12 p.
@article{SDPP_1974-1975__16_2_A12_0,
     author = {Barkan, Philippe},
     title = {Partitions quadratiques et cyclotomie},
     journal = {S\'eminaire Delange-Pisot-Poitou. Th\'eorie des nombres},
     publisher = {Secr\'etariat math\'ematique},
     volume = {16},
     number = {2},
     year = {1974-1975},
     note = {talk:G13},
     zbl = {0324.10037},
     mrnumber = {401632},
     language = {fr},
     url = {http://www.numdam.org/item/SDPP_1974-1975__16_2_A12_0}
}
Barkan, Philippe. Partitions quadratiques et cyclotomie. Séminaire Delange-Pisot-Poitou. Théorie des nombres, Volume 16 (1974-1975) no. 2, Talk no. G13, 12 p. http://www.numdam.org/item/SDPP_1974-1975__16_2_A12_0/

[1] Bachmann (P.). - Die Lehre von der Kreisteilung und ihre Beziehungen zur Zahlentheorie. 2te Auflage. - Leipzig, B. G. Teubner, 1921.

[2] Barrucand (P.) and Cohn (H.). - Note on primes of type x2 + 32y2 , class number, and residuacity, J. für reine und angew. Math., t. 238, 1969, p. 67-70. | MR 249396 | Zbl 0207.36202

[3] Brewer (B.W.). - On certain character sums, Trans. Amer. math. Soc., t. 99, 1961, p. 241-245. | MR 120202 | Zbl 0103.03205

[4] Brewer (B.W.). - On primes of the form u2 + 5v2 , Proc. Amer. math. Soc., t. 17, 1966, p. 502-509. | MR 188171 | Zbl 0147.29801

[5] Cauchy (A.L.). - Mémoire sur la théorie des nombres, "Oeuvres complètes", 1re série, t. 3, p. 5-83. - Paris, Gauthier-Villars, 1911.

[6] Davenport (H.) und Hasse (H.). - Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. für reine und angew. Math., t. 172, 1934, p. 151-182. | JFM 60.0913.01

[7] Dickson (L.E.). - History of the theory of numbers, vol. 3 : Quadratic and higher forms. - Washington, Carnegie Institution, 1923 (réimp. Chelsea, 1971). | JFM 49.0100.12

[8] Dickson (L.E.). - Cyclotomy, higher congruences, and Waring's problem, Amer. J. of Math., t. 57, 1935, p. 391-424 et p. 463-474. | Zbl 0012.01203

[9] Dickson (L.E.). - Cyclotomy and trinomial congruences, Trans. Amer. math. Soc., t. 37, 1935, p. 363-380. | MR 1501791 | Zbl 0011.29301

[10] Dickson (L.E.). - Cyclotomy when e is composite, Trans. Amer. math. Soc., t. 38, 1935, p. 187-200. | MR 1501808 | Zbl 0012.33803

[11] Eisenstein (G.). - Zur Theorie der quadratischen Zerfällung der Primzahlen 8n + 3 , 7n + 2 , und 7n + 4 , J. für reine und angew. Math., t. 37, 1848, p. 97-126. | Zbl 037.1022cj

[12] Gauss (C.F.). - Recherches arithmétiques, Traduites par Poullet-Delisle. - Paris, Courcier, 1807 (Réimp. A. Blanchard, 1953).

[13] Gauss (C.F.). - Werke, t. 2. - Göttingen, Königliche Gesellschaft der Wissenschaften, 1863.

[14] Giudici (R.E.), Muskat (J.B.) and Robinson (S.F.). - On the evaluation of Brewer's character sums, Trans. Amer. math. Soc., t. 171, 1972, p. 317-347. | MR 306122 | Zbl 0249.10031

[15] Hayashi (H.). - On a criterion for power residuacity, Mem. Fac. Sc., Kyushu Univ., Ser. A, t. 27, 1973, p. 211-220. | MR 369229 | Zbl 0272.12005

[16] Jacobi (C.G.J.). - Über die Kreisteilung und ihre Anwendung auf die Zahlentheorie, J. für reine und angew. Math., t. 30, 1846, p. 166-182 ; et "Gesammelte Werke", t. 6, p. 254-274. - Berlin, G. Reimer, 1891. | Zbl 030.0860cj

[17] Jacobsthal (E.). - Über die Darstellung der Primzahlen der Form 4n + 1 als Summe zweier Quadrate, J. für reine und angew. Math., t. 132, 1907, p. 238-245. | JFM 38.0238.03

[18] Kummer (E.E.). - Über die Ergänzzungssätze zu den allgemeinen Reziprozitätsgesetzen, J. für reine und angew. Math., t. 44, 1852, p. 93-146. | Zbl 044.1198cj

[19] Lehmer (E.). - On the quadratic character of some quadratic surds, J. für reine und angew. Math., t. 250, 1971, p. 42-48. | MR 286777 | Zbl 0222.12007

[20] Lehmer (E.). - On the cubic character of quadratic units, J. of number theory, t. 5, 1973, p. 385-389. | MR 321906 | Zbl 0274.12006

[21] Leonard (P.A.) and Williams (K.S.). - The septic character of 2 , 3 , 5 and 7 , Pacific J. of Math., t. 52, 1974, p. 143-147. | MR 364064 | Zbl 0265.10004

[22] Leonard (P.A.) and Williams (K.S.). - A diophantine system of DICKSON, Atti Accad. naz. dei Lincei, Rendiconti, vol. 56, 1974, p. 145-150. | MR 374108 | Zbl 0299.12017

[23] Lienen (H. Von). - Primzahien als achte Potenzreste, J. für reine und angew. Math., t. 266, 1974, p. 107-117. | MR 340160 | Zbl 0279.10003

[24] Muskat (J.B.). - Reciprocity and Jacobi sums, Pacific J. of Math., t. 20, 1967, p. 275-280. | MR 210657 | Zbl 0204.06402

[25] Muskat (J.B.). - On Jacobi sums of certain composite orders, Trans. Amer. math. Soc., t. 134, 1968, p. 483-502. | MR 232752 | Zbl 0174.07701

[26] Muskat (J.B.) and Whiteman (A.L.). - The cyclotomic numbers of order twenty, Acta Arithmetica, Warszawa, t. 17, 1970, p. 185-216. | MR 268151 | Zbl 0216.30801

[27] Muskat (J.B.). - Use of computers in number theory, "Computers in number theory", Edited by A. O. L. Atkin and B. J. Birch, P. 141-147. - New York and London, Academic Press, 1971. | Zbl 0235.12013

[28] Muskat (J.B.) and Zee (Y.C.). - Sign ambiguities of Jacobi sums, Duke Math. J., t. 40, 1973, p. 313-334. | MR 314776 | Zbl 0268.10019

[29] Schrutka (L. Von). - Eine Beweis für die Zerlegbarkeit der Primzahlen von der Form 6n + 1 ein einfaches und ein dreifaches Quadrat, J. für reine und angew. Math., t. 140, 1911, p. 252-265. | JFM 42.0220.02

[30] Stickelberger (L.). - Über eine Verallgemeinerung der Kreisteilung, Math. Annalen, t. 37, 1890, p. 321-367. | JFM 22.0100.01 | MR 1510649

[31] Whiteman (A.L.). - Cyclotomy and Jacobsthal sums, Amer. J. of Math., t. 74, 1952, p. 89-99. | MR 45758 | Zbl 0046.26803

[32] Whiteman (A.L.). - Finite Fourier series and equations in finite fields, Trans. Amer. math. Soc., t. 74, 1953, p. 78-98. | MR 52453 | Zbl 0053.02704

[33] Whiteman (A.L.). - The cyclotomic numbers of order ten, "Combinatorial analysis", p. 95-111. - Providence, American mathematical Society, 1960 (Proceedings of Symposia in applied Mathematics, 10). | MR 113851 | Zbl 0096.02604

[34] Whiteman (A.L.). - Theorems on Brewer and Jacobsthal sums, I, "Theory of numbers", p. 44-55. - Providence, American mathematical Society, 1965 (Proceedings of Symposia in pure Mathematics, 8). | MR 175861 | Zbl 0154.29501

[35] Whiteman (A.L.). - Theorems on Brewer and Jacobsthal sums, II, Michigan math. J., t. 12, 1965, p. 65-80. | MR 217037 | Zbl 0154.29502

[36] Williams K.S.). - Elementary treatment of a quadratic partition of primes p ≡ 1 (mod 7) , Illinois J. of Math., t. 18, 1974, p. 608-621. | Zbl 0292.12022

[37] Yamamoto (K.). - On a conjecture of Hasse concerning multiplicative relations of Gaussian sums, J. Combin. Theory, t. 1, 1966, p. 476-489. | MR 213311 | Zbl 0173.03901

[38] Yamamoto (K.). - On Jacobi sums and difference sets, J. Combin. Theory, t. 3, 1967, p. 146-181. | MR 219500 | Zbl 0171.01102

[39] Zee (Y.C.). - The Jacobi sums of orders thirteen and sixty and related quadratic decompositions, Math. Z., t. 115, 1970, p. 259-272. | MR 262202 | Zbl 0191.33002

[40] Zee (Y.C.). - The Jacobi sums of order twenty-two, Proc. Amer. math. Soc., t. 28, 1971, p. 25-31. | MR 272748 | Zbl 0213.32901