The area of the Mandelbrot set and Zagier's conjecture

TL;DR

This paper proves Zagier's conjecture on the 2-adic valuation of coefficients related to the Mandelbrot set's area, specifically for cases where the index is congruent to 2 modulo 4.

Contribution

It provides a proof of Zagier's conjecture concerning the 2-adic valuation of certain coefficients in the Mandelbrot set area series.

Findings

Confirmed Zagier's conjecture for specific coefficients

Established the 2-adic valuation pattern for these coefficients

Enhanced understanding of the Mandelbrot set's area calculation

Abstract

We prove Zagier's conjecture regarding the 2-adic valuation of the coefficients $\{b_m\}$ that appear in Ewing and Schober's series formula for the area of the Mandelbrot set in the case where $m\equiv 2 \mod 4$.