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3:00pm, Wednesday 5 November 2025

Abstract

In this talk, I will take you on a journey through the character sums of division polynomials evaluated at rational points on elliptic curves over prime fields; a topic that first caught my attention near the end of my PhD, inspired by a 2009 paper of I. E. Shparlinski and K. E. Stange. These character values exhibit an “almost multiplicative” behaviour. Motivated by Chowla’s conjectures on correlations of multiplicative functions, I will first present a recent joint work with I. E. Shparlinski (2025) on the correlations of these character sums under shifts. I will then discuss some bounds for these sums when twisted by various multiplicative functions.