Character sums of Division polynomials twisted by multiplicative functions

2025/08/06 by Bhakta, Subham
#11G07 #11L40 #11N25 #11N60 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.03988

Abstract

Let E be an elliptic curve over the finite field \mathbbF_p, and P ∈ E(\mathbbF_p) be an \mathbbF_p-rational point. We obtain nontrivial estimates for multiplicative character sums associated with the division polynomials ψ_n(P) twisted by several multiplicative functions, where ψ_n(P) denotes the n-th division polynomial evaluated at P.

Citations

• On the Dynamical System Generated by the Möbius Transformation at Smooth Times
• On the correlations between character sums of division polynomials under shifts
• Sums of Kloosterman sums over square-free and smooth integers
• The elliptic sieve and Brauer groups
• Divisor-bounded multiplicative functions in short intervals

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