On the 2 k -th power mean of the quadratic character sums of the polynomials

Puntos clave

• The central aim is to explore the 2k-th power mean of quadratic character sums of polynomials using known results from elliptic curves.
• Utilized known results on elliptic curves over fixed prime fields.
• Applied elementary methods in analysis of quadratic character sums.
• Developed exact calculation formulas and a general asymptotic formula.
• Provided exact formulas for the 2k-th power mean of quadratic character sums.
• Derived a general asymptotic formula applicable to these sums.