Gauss Sums of Cubic Characters over p r , p Odd

Davide Schipani; Michele Elia

Bulletin of the Polish Academy of Sciences. Mathematics (2012)

  • Volume: 60, Issue: 1, page 1-19
  • ISSN: 0239-7269

Abstract

top
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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.