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On some problems on the distribution of digits of integers

2019-10-09 15:14

报告人: Thomas Stoll

报告人单位: Universitè de Lorraine

时间: 2019-10-12 9:30-10:30

地点: 卫津路校区6号楼112教

开始时间: 9:30

报告人简介: 教授

年: 2019

日月: 10.12

For $\leq $, let $S_q (n)$ denote the sum of digits of an integer $n$ in the base $q$ expansion. Answering, in an extended form, a question of Deshouillers, Habsieger, Laishram, and Landreau, we show that, provided $a$ and $b$ are multiplicatively independent, any positive real number is a limit point of the sequence $\{ S_b (n) / S_a (n)\} _ {n \leq 1}$ . We also provide bounds for the counting functions of the corresponding subsequences. The proof uses exponential sums, discrepancy estimates and transcendence theory. This is joint work with R. de la Bretèche and G. Tenenbaum.

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