Applications of some exponential sums on prime powers: a survey

1. Introduction

2. Statements

3. Settings for Theorems 2.1 and 2.4-2.6

4. General results on $\widetilde{S}_{\ell}(\alpha)$ and $S_{\ell}(\alpha)$ and motivations

5. Settings for Theorems 2.2-2.3

6. Corrigendum of [17] and of [19]