On the determination of Gauss sums

John H. Loxton

Séminaire Delange-Pisot-Poitou. Théorie des nombres (1976-1977)

  • Volume: 18, Issue: 2, page 1-12

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Loxton, John H.. "On the determination of Gauss sums." Séminaire Delange-Pisot-Poitou. Théorie des nombres 18.2 (1976-1977): 1-12. <http://eudml.org/doc/110982>.

@article{Loxton1976-1977,
author = {Loxton, John H.},
journal = {Séminaire Delange-Pisot-Poitou. Théorie des nombres},
language = {eng},
number = {2},
pages = {1-12},
publisher = {Secrétariat mathématique},
title = {On the determination of Gauss sums},
url = {http://eudml.org/doc/110982},
volume = {18},
year = {1976-1977},
}

TY - JOUR
AU - Loxton, John H.
TI - On the determination of Gauss sums
JO - Séminaire Delange-Pisot-Poitou. Théorie des nombres
PY - 1976-1977
PB - Secrétariat mathématique
VL - 18
IS - 2
SP - 1
EP - 12
LA - eng
UR - http://eudml.org/doc/110982
ER -

References

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  1. [1] Cassels ( J.W.S. ) . - On the determination of generalised Gauss sums, Archiv. Math., Brno, t. 5, 1969, p. 79-84. Zbl0233.10018MR294266
  2. [2] Cassels ( J.W.S.). - On Kummer sums, Proc. London math. Soc., Series 3, t. 21, 1970, p. 19-27. Zbl0197.32004MR266895
  3. [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. [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. 
  5. [5] Gauss ( C.F. ). - Disquisitiones Arithmeticae.-Lipsiae, G. Fleischer, 1801. 
  6. [6] Gauss ( C.F. ). - Summatio quarundarum serierum singularium, Commentationes societatis regiae Gottingensis recentiores, Band 1, 1811. 
  7. [7] Goldstine ( H.) and Neumann ( J. von). - A numerical study of a conjecture of Kummer, Math. of Comp., t. 7, 1953, p. 133-134. Zbl0051.28101MR55784
  8. [8] Hasse ( H.). - Vorlesungen über Zahlentheorie. 2nd ed. - Berlin, Springer-Verlag, 1964. Zbl0123.04201MR188128
  9. [9] Kubota ( T.). - On a special kind of Dirichlet series, J. Math. Soc. Japan, t. 20, 1968, p. 193-207. Zbl0157.10202MR228455
  10. [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). Zbl0215.36103MR340221
  11. [11] Kummer ( E.E.). - De residuis cubicis disquisitiones nonnullae analyticae, J. reine und angew. Math., t. 32, 1846, p. 341-359. 
  12. [12] Lebesgue ( V.-A.). - Sommation de quelques séries, J. de Math. pures et appl., Série 1, t. 5, 1840, p. 42-71. 
  13. [13] Lehmer ( E.). - On the location of Gauss sums, Math. of Comp., t. 10, 1956, p. 194-202. Zbl0073.03001MR86092
  14. [14] Loxton ( J.H.). - Products related to Gauss sums, J. reine und angew. Math., t. 268/269, 1974, p. 53-67. Zbl0293.10019MR344205
  15. [15] Loxton ( J.H.). - Some conjectures concerning Gauss sums, J. reine und angew. Math. (to appear). Zbl0362.10033MR460250
  16. [16] McGettrick ( A.D.). - On the biquadratic Gauss sum, Proc. Camb. phil. Soc., t. 71, 1972, p. 79-83. Zbl0226.10042MR289427
  17. [17] Moreno ( C.J.). - Sur le problème de Kummer, Enseign. Nath., t. 20, 1974, p. 45-51. Zbl0307.12004MR374057
  18. [18] Odoni ( R.K.). - On Gauss sums (mod pn) , n ≥ 2 , Bull. London math. Soc. , t. 5, 1973, p. 325-327. Zbl0269.10020
  19. [19] Patterson ( S.J.). - A cubic analogue of the theta series, J. reine und angew. Math. (to appear). Zbl0358.10011MR563068
  20. [20] Reshetukha ( I.V.). - A problem in the theory of cubic sums, Mat. Zametki, t. 7, 1970, p. 469-476. 
  21. [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. MR176097
  22. [22] Yamamoto ( K.). - On Gaussian sums with biquadratic residue characters, J. reine und angew. Math., t. 219, 1965, p. 200-213. Zbl0133.29306MR184919

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