Corrigendum to ‘On the convergence of diophantine Dirichlet series’, Proc. Edinb. Math. Soc. 55 (2012), 513–541

Proceedings of the Edinburgh Mathematical Society

article

Tanguy Rivoal¹ 

[1] Institut Fourier

DOI  :  10.1017/S0013091521000195

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

I recently discovered that the proof of Proposition 3.1 in my 2012 paper 1[1] (stated on page 522) is not correct. The proof can be corrected but this introduces a factor on the left-hand side of Equation (3.2). This factor is not important for Proposition 3.1 itself but it is important for its applications. Unfortunately, it invalidates the end of the proof of Theorem 1.1. I could not find a complete correction for it, and I present a slightly weaker statement below. On the other hand, the statements of Theorems 1.2 and 1.3 are not modified because their proofs are not affected in a crucial way by this factor. I use the notation and labels of the paper. These labels are of the form (a.b) with a ≥ 1. There will be no confusion with the labels of this corrigendum which are the form (a.b) with a = 0. For the properties of continued fractions, I refer to §1.1 of the paper.

【 授权许可】

CC BY