What question did this study set out to answer?

The research aims to estimate multiplicative character sums related to division polynomials of elliptic curves.

March 28, 2026Canadian Mathematical Bulletin0 citationsOpen Access

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

Abstract

Let E be an elliptic curve over the finite field F p , and P P EpF p q be an F p -rational point.We obtain nontrivial estimates for multiplicative character sums associated with the division polynomials n pP q twisted by several multiplicative functions, where n pP q denotes the n-th division polynomial evaluated at P .

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