On the determination of Gauss sums
Séminaire Delange-Pisot-Poitou. Théorie des nombres, Tome 18 (1976-1977) no. 2, Exposé no. 27, 12 p.
@article{SDPP_1976-1977__18_2_A8_0,
     author = {Loxton, John H.},
     title = {On the determination of {Gauss} sums},
     journal = {S\'eminaire Delange-Pisot-Poitou. Th\'eorie des nombres},
     note = {talk:27},
     pages = {1--12},
     publisher = {Secr\'etariat math\'ematique},
     volume = {18},
     number = {2},
     year = {1976-1977},
     mrnumber = {551351},
     zbl = {0373.10023},
     language = {en},
     url = {http://archive.numdam.org/item/SDPP_1976-1977__18_2_A8_0/}
}
TY  - JOUR
AU  - Loxton, John H.
TI  - On the determination of Gauss sums
JO  - Séminaire Delange-Pisot-Poitou. Théorie des nombres
N1  - talk:27
PY  - 1976-1977
SP  - 1
EP  - 12
VL  - 18
IS  - 2
PB  - Secrétariat mathématique
UR  - http://archive.numdam.org/item/SDPP_1976-1977__18_2_A8_0/
LA  - en
ID  - SDPP_1976-1977__18_2_A8_0
ER  - 
%0 Journal Article
%A Loxton, John H.
%T On the determination of Gauss sums
%J Séminaire Delange-Pisot-Poitou. Théorie des nombres
%Z talk:27
%D 1976-1977
%P 1-12
%V 18
%N 2
%I Secrétariat mathématique
%U http://archive.numdam.org/item/SDPP_1976-1977__18_2_A8_0/
%G en
%F SDPP_1976-1977__18_2_A8_0
Loxton, John H. On the determination of Gauss sums. Séminaire Delange-Pisot-Poitou. Théorie des nombres, Tome 18 (1976-1977) no. 2, Exposé no. 27, 12 p. http://archive.numdam.org/item/SDPP_1976-1977__18_2_A8_0/

[1] Cassels (J.W.S. ) . - On the determination of generalised Gauss sums, Archiv. Math., Brno, t. 5, 1969, p. 79-84. | MR | Zbl

[2] Cassels (J.W.S.). - On Kummer sums, Proc. London math. Soc., Series 3, t. 21, 1970, p. 19-27. | MR | Zbl

[3] Cauchy (A.). - Méthode simple et nouvelle pour la détermination complète des sommes alternées formées avec les racines primitives des equations binômes, J. de Math. pures et appl., Série 1, t. 5, 1840, p. 154-168.

[4] Eisenstein (G. ). - Beitrage zur Theorie der elliptischen Functionen, I : Ableitung des biquadratischen Fundamental theorems aus der Theorie der Lemniskatenfunctionen, nebst Bemerkungen zu den Transformationsformeln, J. reine und angew. Math., t. 30, 1846, p. 185-210. | Zbl

[5] Gauss (C.F. ). - Disquisitiones Arithmeticae.-Lipsiae, G. Fleischer, 1801.

[6] Gauss (C.F. ). - Summatio quarundarum serierum singularium, Commentationes societatis regiae Gottingensis recentiores, Band 1, 1811.

[7] Goldstine (H.) and Neumann (J. Von). - A numerical study of a conjecture of Kummer, Math. of Comp., t. 7, 1953, p. 133-134. | MR | Zbl

[8] Hasse (H.). - Vorlesungen über Zahlentheorie. 2nd ed. - Berlin, Springer-Verlag, 1964. | MR | Zbl

[9] Kubota (T.). - On a special kind of Dirichlet series, J. Math. Soc. Japan, t. 20, 1968, p. 193-207. | MR | Zbl

[10] Kubota (T.). - Some results concerning reciprocity law and real automorphic functions, "1969 Number theory institute", p. 382-395. - Providence, American mathematical Society, 1971 (Proceedings of Symposia in pure Mathematics, 20). | MR | Zbl

[11] Kummer (E.E.). - De residuis cubicis disquisitiones nonnullae analyticae, J. reine und angew. Math., t. 32, 1846, p. 341-359. | Zbl

[12] Lebesgue (V.-A.). - Sommation de quelques séries, J. de Math. pures et appl., Série 1, t. 5, 1840, p. 42-71.

[13] Lehmer (E.). - On the location of Gauss sums, Math. of Comp., t. 10, 1956, p. 194-202. | MR | Zbl

[14] Loxton (J.H.). - Products related to Gauss sums, J. reine und angew. Math., t. 268/269, 1974, p. 53-67. | MR | Zbl

[15] Loxton (J.H.). - Some conjectures concerning Gauss sums, J. reine und angew. Math. (to appear). | MR | Zbl

[16] Mcgettrick (A.D.). - On the biquadratic Gauss sum, Proc. Camb. phil. Soc., t. 71, 1972, p. 79-83. | MR | Zbl

[17] Moreno (C.J.). - Sur le problème de Kummer, Enseign. Nath., t. 20, 1974, p. 45-51. | MR | Zbl

[18] Odoni (R.K.). - On Gauss sums (mod pn) , n ≥ 2 , Bull. London math. Soc. , t. 5, 1973, p. 325-327. | Zbl

[19] Patterson (S.J.). - A cubic analogue of the theta series, J. reine und angew. Math. (to appear). | MR | Zbl

[20] Reshetukha (I.V.). - A problem in the theory of cubic sums, Mat. Zametki, t. 7, 1970, p. 469-476.

[21] Selberg (A.). - Discontinuous groups and harmonic analysis, "Proceedings of the international Congress of mathematicians [1962. Stockholm]", p. 177-189. - Djursholm, Institut Mittag-Leffler, 1963. | MR

[22] Yamamoto (K.). - On Gaussian sums with biquadratic residue characters, J. reine und angew. Math., t. 219, 1965, p. 200-213. | MR | Zbl