An elementary approach is shown which derives the values of the Gauss sums over F_(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 then are 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 p-th roots ofunity.

Gauss Sums of Cubic Characters over F_(p^m),, p Odd / Schipani, D.; Elia, Michele. - In: BULLETIN OF THE POLISH ACADEMY OF SCIENCES. MATHEMATICS. - ISSN 0239-7269. - STAMPA. - 60:1(2012), pp. 1-19. [10.4064/ba60-1-1]

Gauss Sums of Cubic Characters over F_(p^m),, p Odd

ELIA, Michele
2012

Abstract

An elementary approach is shown which derives the values of the Gauss sums over F_(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 then are 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 p-th roots ofunity.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2496725
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo