Gauss Sums of Cubic Characters over ${}_{p^r}$, p Odd

Davide Schipani, and Michele Elia. "Gauss Sums of Cubic Characters over $_{p^r}$, p Odd." Bulletin of the Polish Academy of Sciences. Mathematics 60.1 (2012): 1-19. <http://eudml.org/doc/281345>.

@article{DavideSchipani2012,
abstract = {An elementary approach is shown which derives the values of the Gauss sums over $_\{p^r\}$, p odd, of a cubic character. New links between Gauss sums over different field extensions are shown in terms of factorizations of the Gauss sums themselves, which are then revisited in terms of prime ideal decompositions. Interestingly, one of these results gives a representation of primes p of the form 6k+1 by a binary quadratic form in integers of a subfield of the cyclotomic field of the pth roots of unity.},
author = {Davide Schipani, Michele Elia},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {cubic Gauss sum; cyclotomy},
language = {eng},
number = {1},
pages = {1-19},
title = {Gauss Sums of Cubic Characters over $_\{p^r\}$, p Odd},
url = {http://eudml.org/doc/281345},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Davide Schipani
AU - Michele Elia
TI - Gauss Sums of Cubic Characters over $_{p^r}$, p Odd
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 1
SP - 1
EP - 19
AB - An elementary approach is shown which derives the values of the Gauss sums over $_{p^r}$, p odd, of a cubic character. New links between Gauss sums over different field extensions are shown in terms of factorizations of the Gauss sums themselves, which are then revisited in terms of prime ideal decompositions. Interestingly, one of these results gives a representation of primes p of the form 6k+1 by a binary quadratic form in integers of a subfield of the cyclotomic field of the pth roots of unity.
LA - eng
KW - cubic Gauss sum; cyclotomy
UR - http://eudml.org/doc/281345
ER -