The cyclotomic numbers of order fifteen
Authors:
Nicholas Buck, Lones Smith, Blair K. Spearman and Kenneth S. Williams
Journal:
Math. Comp. 48 (1987), 67-83
MSC:
Primary 11B83; Secondary 11T21
DOI:
https://doi.org/10.1090/S0025-5718-1987-0866099-5
MathSciNet review:
866099
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Explicit formulae are obtained for the cyclotomic numbers of order 15.
- [1] Helen Popova Alderson, On the septimic character of 2 and 3, Proc. Cambridge Philos. Soc. 74 (1973), 421–433. MR 323763, https://doi.org/10.1017/s030500410007715x
- [2] L. D. Baumert and H. Fredricksen, The cyclotomic numbers of order eighteen with applications to difference sets, Math. Comp. 21 (1967), 204–219. MR 223322, https://doi.org/10.1090/S0025-5718-1967-0223322-5
- [3] H. Davenport & H. Hasse, "Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen," J. Reine Angew. Math., v. 172, 1934, pp. 151-182.
- [4] L. E. Dickson, Cyclotomy, Higher Congruences, and Waring’s Problem, Amer. J. Math. 57 (1935), no. 2, 391–424. MR 1507083, https://doi.org/10.2307/2371217
- [5] L. E. Dickson, Cyclotomy when 𝑒 is composite, Trans. Amer. Math. Soc. 38 (1935), no. 2, 187–200. MR 1501808, https://doi.org/10.1090/S0002-9947-1935-1501808-6
- [6] Ronald J. Evans and Jay Roderick Hill, The cyclotomic numbers of order sixteen, Math. Comp. 33 (1979), no. 146, 827–835. MR 521298, https://doi.org/10.1090/S0025-5718-1979-0521298-2
- [7] R. J. Evans, "Table of cyclotomic numbers of order twenty-four," Math. Comp., v. 35, 1980, Review 12, pp. 1036-1038.
- [8] Christian Friesen, Joseph B. Muskat, Blair K. Spearman, and Kenneth S. Williams, Cyclotomy of order 15 over 𝐺𝐹(𝑝²),𝑝=4,11(𝑚𝑜𝑑15), Internat. J. Math. Math. Sci. 9 (1986), no. 4, 665–704. MR 870524, https://doi.org/10.1155/S0161171286000832
- [9] Reinaldo E. Giudici, Joseph B. Muskat, and Stanley F. Robinson, On the evaluation of Brewer’s character sums, Trans. Amer. Math. Soc. 171 (1972), 317–347. MR 306122, https://doi.org/10.1090/S0002-9947-1972-0306122-5
- [10] Emma Lehmer, On the number of solutions of 𝑢^{𝑘}+𝐷≡𝑤²(\mod𝑝), Pacific J. Math. 5 (1955), 103–118. MR 67918
- [11] Philip A. Leonard and Kenneth S. Williams, The cyclotomic numbers of order seven, Proc. Amer. Math. Soc. 51 (1975), 295–300. MR 371868, https://doi.org/10.1090/S0002-9939-1975-0371868-8
- [12] Philip A. Leonard and Kenneth S. Williams, The cyclotomic numbers of order eleven, Acta Arith. 26 (1974/75), no. 4, 365–383. MR 376513, https://doi.org/10.4064/aa-26-4-365-383
- [13] J. B. Muskat, The cyclotomic numbers of order fourteen, Acta Arith. 11 (1965/66), 263–279. MR 193081, https://doi.org/10.4064/aa-11-3-263-279
- [14] Joseph B. Muskat, On Jacobi sums of certain composite orders, Trans. Amer. Math. Soc. 134 (1969), 483–502. MR 232752, https://doi.org/10.1090/S0002-9947-1968-0232752-4
- [15] Joseph B. Muskat and Albert L. Whiteman, The cyclotomic numbers of order twenty, Acta Arith. 17 (1970), 185–216. MR 268151, https://doi.org/10.4064/aa-17-2-185-216
- [16] Joseph B. Muskat and Yun Cheng Zee, On the uniqueness of solutions of certain Diophantine equations, Proc. Amer. Math. Soc. 49 (1975), 13–19. MR 360461, https://doi.org/10.1090/S0002-9939-1975-0360461-9
- [17] Albert Leon Whiteman, The cyclotomic numbers of order sixteen, Trans. Amer. Math. Soc. 86 (1957), 401–413. MR 92807, https://doi.org/10.1090/S0002-9947-1957-0092807-7
- [18] Albert Leon Whiteman, The cyclotomic numbers of order ten, Proc. Sympos. Appl. Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960, pp. 95–111. MR 0113851
- [19] A. L. Whiteman, The cyclotomic numbers of order twelve, Acta Arith. 6 (1960), 53–76. MR 118709, https://doi.org/10.4064/aa-6-1-53-76
, 
," Internat. J. Math. Math. Sci. (To appear.) 
," Pacific J. Math., v. 5, 1955, pp. 103-118. Retrieve articles in Mathematics of Computation with MSC: 11B83, 11T21
Retrieve articles in all journals with MSC: 11B83, 11T21
Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1987-0866099-5
Article copyright:
© Copyright 1987
American Mathematical Society
