On the correlations between character sums of division polynomials under shifts

2025/07/12 by Subham Bhakta, Bhakta, Subham, Igor E. Shparlinski +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #11G07 #11L40 #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2507.09271

openalex publication_date 2025/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 study the sums S_χ,P(N,h) = ∑_n=1^N χ(ψ_n(P)) χ(ψ_n+h(P)), where ψ_n(P) denotes the n-th division polynomial evaluated at P, and χ is a multiplicative character of \mathbbF_p^*. We estimate S_χ,P(N,h) on average over h over a rather short interval h ∈ [1, H]. We also obtain a multidimensional generalisation of this result.

Citations

• Equivalence of the logarithmically averaged Chowla and Sarnak conjectures

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• Character sums of Division polynomials twisted by multiplicative functions

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