Numerical Experiments for Erdős Problem 513: Maximum Term vs. Maximum Modulus for Entire Functions (Colab Notebook + Data)

This deposit contains reproducible code and computational assets accompanying the note\emph{A Schur-class viewpoint on an Erd\H{o}s problem on maximum terms of transcendental entire functions}by Zeraoulia Rafik. \textbf{Problem context.}For an entire function $f(z)=\sum_{n\ge 0} a_n z^n$, define$M(r):=\max_{|z|=r}|f(z)|$ and $\mu(r):=\max_{n\ge 0}|a_n|r^n$.Erd\H{o}s Problem~513 asks for the greatest possible value of$\Lambda=\sup_f\liminf_{r\to\infty}\mu(r)/M(r)$ over transcendental entire functions. \textbf{Contents.}The archive includes:\begin{itemize}\item a Google Colab compatible notebook (\texttt{erdos513\_numerics\_colab.ipynb});\item scripts/cells to generate exact plots and tables for a tuned lacunary ``control experiment'';\item pre-generated figures used in the manuscript (PNG format);\item utilities for stable evaluation of $\mu(r)$ and for approximating $M(r)$ for general coefficientsvia angular sampling / FFT (exploratory).\end{itemize} \textbf{Key computational experiment.}The tuned lacunary experiment constructs positive-coefficient lacunary series$f(z)=\sum_{k=0}^{K}A_k z^{2^k}$ with coefficients chosen so that consecutive terms tie at prescribedradii $R_k=2^{k+1}$. Since coefficients are positive, $M(r)=f(r)$ for $r>0$, and $\mu(r)/M(r)$ is computed\emph{exactly}. The data illustrate persistent dips $\mu(R_k)/M(R_k)\approx 1/2$ at extremely large radii(exceeding $10^{15}$ for $K=50$), clarifying the mechanism behind the baseline value $1/2$. \textbf{Reproducibility.}All figures and tables in the numerical section of the note can be regenerated by running the notebook.The code is intended as a diagnostic and exploration tool (not a proof of the liminf constant $\Lambda$).