Geodesic
Calculation of a Gauss sum via the discrete Fourier transform
Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 1, pp. 90-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

The explicit formula for a Gauss sum is proved using the discrete Fourier transform. The Gauss quadratic reciprocity law is established as a corollary. 
@article{DVMG_2014_14_1_a7,
     author = {A. V. Ustinov},
     title = {Calculation of a {Gauss} sum via the discrete {Fourier} transform},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {90--95},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a7/}
}
TY  - JOUR
AU  - A. V. Ustinov
TI  - Calculation of a Gauss sum via the discrete Fourier transform
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2014
SP  - 90
EP  - 95
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a7/
LA  - ru
ID  - DVMG_2014_14_1_a7
ER  - 
%0 Journal Article
%A A. V. Ustinov
%T Calculation of a Gauss sum via the discrete Fourier transform
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2014
%P 90-95
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a7/
%G ru
%F DVMG_2014_14_1_a7
A. V. Ustinov. Calculation of a Gauss sum via the discrete Fourier transform. Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 1, pp. 90-95. http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a7/

[1] N. V. Budarina, V. A. Bykovskii, “Arifmeticheskaya priroda tozhdestv dlya troinogo i pyatikratnogo proizvedenii”, Dalnevost. matem. zhurn., 11:2 (2011), 140–148 | MR

[2] P. G. L. Dirikhle, Lektsii po teorii chisel, ONTI MKTP, 1936

[3] G. Devenport, Multiplikativnaya teoriya chisel, Nauka, Moskva, 1971 | MR

[4] N. M. Korobov, Trigonometricheskie summy i ikh prilozheniya, Nauka, M., 1989 | MR | Zbl

[5] N. M. Korobov, “Spetsialnye polinomy i ikh prilozheniya Diofantovy priblizheniya”, Matem. Zapiski, 2 (1996), 77–89 | MR

[6] Math. Notes, 73:1 (2003), 97–102 | DOI | DOI | MR | Zbl

[7] A. V. Ustinov, “Elementarnyi podkhod k vychisleniyu $\zeta(2n)$”, Chebyshevskii sbornik, 4 (2003), 106–110 | MR | Zbl