General Jacobi Sums And Its Applications

This dissertation puts Traces function in the condition of classical Jacobi sums to get a general Jacobi sums,in this way,the general Jacobi sums can be used in more area.It is not hard to see that the general Jacobi sums satisfies all properties of the classical one.The general Jacobi sums can also be presented with Gauss sums,like the classical one.So the general Jacobi sums has a great structure.Using the properties of general JAcobi sums,we can get any general Jacobi sums by knowing the value of general Jacobi with one character and the classical Jacobi sums with two characters.It make geting the value of general Jacobi sums simpler.And in the end of the article,we give an example for the General Jacobi sums.