@article{SDPP_1974-1975__16_2_A12_0,
author = {Barkan, Philippe},
title = {Partitions quadratiques et cyclotomie},
journal = {S\'eminaire Delange-Pisot-Poitou},
note = {talk:G13},
pages = {G1--G12},
year = {1974-1975},
publisher = {Secr\'etariat math\'ematique},
volume = {16},
number = {2},
mrnumber = {401632},
zbl = {0324.10037},
language = {fr},
url = {https://www.numdam.org/item/SDPP_1974-1975__16_2_A12_0/}
}
TY - JOUR AU - Barkan, Philippe TI - Partitions quadratiques et cyclotomie JO - Séminaire Delange-Pisot-Poitou N1 - talk:G13 PY - 1974-1975 SP - G1 EP - G12 VL - 16 IS - 2 PB - Secrétariat mathématique UR - https://www.numdam.org/item/SDPP_1974-1975__16_2_A12_0/ LA - fr ID - SDPP_1974-1975__16_2_A12_0 ER -
Barkan, Philippe. Partitions quadratiques et cyclotomie. Séminaire Delange-Pisot-Poitou, Tome 16 (1974-1975) no. 2, Exposé no. G13, 12 p.. https://www.numdam.org/item/SDPP_1974-1975__16_2_A12_0/
[1] . - Die Lehre von der Kreisteilung und ihre Beziehungen zur Zahlentheorie. 2te Auflage. - Leipzig, B. G. Teubner, 1921.
[2] and . - Note on primes of type x2 + 32y2 , class number, and residuacity, J. für reine und angew. Math., t. 238, 1969, p. 67-70. | Zbl | MR
[3] . - On certain character sums, Trans. Amer. math. Soc., t. 99, 1961, p. 241-245. | Zbl | MR
[4] . - On primes of the form u2 + 5v2 , Proc. Amer. math. Soc., t. 17, 1966, p. 502-509. | Zbl | MR
[5] . - Mémoire sur la théorie des nombres, "Oeuvres complètes", 1re série, t. 3, p. 5-83. - Paris, Gauthier-Villars, 1911.
[6] und . - Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. für reine und angew. Math., t. 172, 1934, p. 151-182. | JFM
[7] . - History of the theory of numbers, vol. 3 : Quadratic and higher forms. - Washington, Carnegie Institution, 1923 (réimp. Chelsea, 1971). | JFM
[8] . - Cyclotomy, higher congruences, and Waring's problem, Amer. J. of Math., t. 57, 1935, p. 391-424 et p. 463-474. | Zbl
[9] . - Cyclotomy and trinomial congruences, Trans. Amer. math. Soc., t. 37, 1935, p. 363-380. | Zbl | MR
[10] . - Cyclotomy when e is composite, Trans. Amer. math. Soc., t. 38, 1935, p. 187-200. | Zbl | MR
[11] . - 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
[12] . - Recherches arithmétiques, Traduites par Poullet-Delisle. - Paris, Courcier, 1807 (Réimp. A. Blanchard, 1953).
[13] . - Werke, t. 2. - Göttingen, Königliche Gesellschaft der Wissenschaften, 1863.
[14] , and . - On the evaluation of Brewer's character sums, Trans. Amer. math. Soc., t. 171, 1972, p. 317-347. | Zbl | MR
[15] . - On a criterion for power residuacity, Mem. Fac. Sc., Kyushu Univ., Ser. A, t. 27, 1973, p. 211-220. | Zbl | MR
[16] . - 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
[17] . - 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
[18] . - Über die Ergänzzungssätze zu den allgemeinen Reziprozitätsgesetzen, J. für reine und angew. Math., t. 44, 1852, p. 93-146. | Zbl
[19] . - On the quadratic character of some quadratic surds, J. für reine und angew. Math., t. 250, 1971, p. 42-48. | Zbl | MR
[20] . - On the cubic character of quadratic units, J. of number theory, t. 5, 1973, p. 385-389. | Zbl | MR
[21] and . - The septic character of 2 , 3 , 5 and 7 , Pacific J. of Math., t. 52, 1974, p. 143-147. | Zbl | MR
[22] and . - A diophantine system of DICKSON, Atti Accad. naz. dei Lincei, Rendiconti, vol. 56, 1974, p. 145-150. | Zbl | MR
[23] . - Primzahien als achte Potenzreste, J. für reine und angew. Math., t. 266, 1974, p. 107-117. | Zbl | MR
[24] . - Reciprocity and Jacobi sums, Pacific J. of Math., t. 20, 1967, p. 275-280. | Zbl | MR
[25] . - On Jacobi sums of certain composite orders, Trans. Amer. math. Soc., t. 134, 1968, p. 483-502. | Zbl | MR
[26] and . - The cyclotomic numbers of order twenty, Acta Arithmetica, Warszawa, t. 17, 1970, p. 185-216. | Zbl | MR
[27] . - 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
[28] and . - Sign ambiguities of Jacobi sums, Duke Math. J., t. 40, 1973, p. 313-334. | Zbl | MR
[29] . - 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
[30] . - Über eine Verallgemeinerung der Kreisteilung, Math. Annalen, t. 37, 1890, p. 321-367. | MR | JFM
[31] . - Cyclotomy and Jacobsthal sums, Amer. J. of Math., t. 74, 1952, p. 89-99. | Zbl | MR
[32] . - Finite Fourier series and equations in finite fields, Trans. Amer. math. Soc., t. 74, 1953, p. 78-98. | Zbl | MR
[33] . - The cyclotomic numbers of order ten, "Combinatorial analysis", p. 95-111. - Providence, American mathematical Society, 1960 (Proceedings of Symposia in applied Mathematics, 10). | Zbl | MR
[34] . - 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). | Zbl | MR
[35] . - Theorems on Brewer and Jacobsthal sums, II, Michigan math. J., t. 12, 1965, p. 65-80. | Zbl | MR
[36] . - Elementary treatment of a quadratic partition of primes p ≡ 1 (mod 7) , Illinois J. of Math., t. 18, 1974, p. 608-621. | Zbl
[37] . - On a conjecture of Hasse concerning multiplicative relations of Gaussian sums, J. Combin. Theory, t. 1, 1966, p. 476-489. | Zbl | MR
[38] . - On Jacobi sums and difference sets, J. Combin. Theory, t. 3, 1967, p. 146-181. | Zbl | MR
[39] . - The Jacobi sums of orders thirteen and sixty and related quadratic decompositions, Math. Z., t. 115, 1970, p. 259-272. | Zbl | MR
[40] . - The Jacobi sums of order twenty-two, Proc. Amer. math. Soc., t. 28, 1971, p. 25-31. | Zbl | MR





