Character Sums of Division Polynomials Twisted by Multiplicative Functions

Key Points

• The research aims to estimate multiplicative character sums related to division polynomials of elliptic curves.
• Analyzed character sums linked to division polynomials
• Focused on elliptic curves over finite fields
• Utilized multiple multiplicative functions to twist these sums
• Obtained nontrivial estimates for the character sums
• Showed that the twist by multiplicative functions alters the estimates significantly
• Provided insights into the behavior of division polynomials under these twists