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In mathematics, an elliptic Gauss sum is an analog of a Gauss sum depending on an elliptic curve with complex multiplication. The quadratic residue symbol in a Gauss sum is replaced by a higher residue symbol such as a cubic or quartic residue symbol, and the exponential function in a Gauss sum is replaced by an elliptic function. They were introduced by Eisenstein ( 1850), at least in the lemniscate case when the elliptic curve has complex multiplication by i, but seem to have been forgotten or ignored until the paper ( Pinch 1988).
( Lemmermeyer 2000, 9.3) gives the following example of an elliptic Gauss sum, for the case of an elliptic curve with complex multiplication by i.
where
![]() | This article includes a
list of references,
related reading, or
external links, but its sources remain unclear because it lacks
inline citations. (June 2020) |
In mathematics, an elliptic Gauss sum is an analog of a Gauss sum depending on an elliptic curve with complex multiplication. The quadratic residue symbol in a Gauss sum is replaced by a higher residue symbol such as a cubic or quartic residue symbol, and the exponential function in a Gauss sum is replaced by an elliptic function. They were introduced by Eisenstein ( 1850), at least in the lemniscate case when the elliptic curve has complex multiplication by i, but seem to have been forgotten or ignored until the paper ( Pinch 1988).
( Lemmermeyer 2000, 9.3) gives the following example of an elliptic Gauss sum, for the case of an elliptic curve with complex multiplication by i.
where