On l-adic logarithms of Gauss sums

For the Gauss sum S( chi ) corresponding to a character chi of order l super(m)d of the multiplicative group of a finite field F sub(q) of characteristic p, we obtain an approximate formula for the l-adic logarithm of S( chi ). We construct a special basis in the group of logarithms and define modul...

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Bibliographic Details
Published in:Izvestiya. Mathematics 2014-01, Vol.78 (3), p.531-553
Main Author: Kuz'min, L V
Format: Article
Language:English
Subjects:
Approximation
Construction
Logarithms
Mathematical analysis
Residues
Sums
Online Access:Get full text
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Summary:For the Gauss sum S( chi ) corresponding to a character chi of order l super(m)d of the multiplicative group of a finite field F sub(q) of characteristic p, we obtain an approximate formula for the l-adic logarithm of S( chi ). We construct a special basis in the group of logarithms and define modulo l super(m) the coefficients of log sub(l)(S( chi )) relative to this basis (modulo l super(m-1) if l = 2). These coefficients are defined in terms of power residues of some cyclotomic numbers at the places over p.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM2014v078n03ABEH002697