Gauss sum
Let be a prime. Let be any multiplicative group character on (that is, any group homomorphism of multiplicative groups ). For any , the complex number
is called a Gauss sum on associated to .
In general, the equation (for nontrivial and ) reduces the computation of general Gauss sums to that of . The absolute value of is always as long as is nontrivial, and if is a quadratic character (that is, is the Legendre symbol ), then the value of the Gauss sum is known to be
References
- 1 Kenneth Ireland & Michael Rosen, A Classical Introduction to Modern Number Theory, Second Edition, Springer–Verlag, 1990.
Title | Gauss sum |
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Canonical name | GaussSum |
Date of creation | 2013-03-22 12:48:28 |
Last modified on | 2013-03-22 12:48:28 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 7 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 11L05 |
Related topic | KloostermanSum |