Large and moderate deviation principles for the Erdős-Kac theorem in function fields
Let \(U_n\) be a random integer chosen uniformly from \(\{1, 2,\dots, n\}\) and \(X_n\) denote the number of distinct prime divisors of \(U_n\). Erdős-Kac theorem asserts that, for any \(a<b\), \[ \lim_{n\to\infty}\mathbf{P}\left(\frac{X_n-\log\log n}{\sqrt{\log\log n}}\in(a,b]\right)=\frac{1}{\sqrt{2\pi}}\int_a^b e^{-\frac{x^2}{2}}dx. \] In the paper under review the authors prove the large and moderate deviation principles for the Erdős-Kac theorem in the polynomial rings of finite fields.
scientific article; zbMATH DE number 7259032
scientific article