Abstract
Abstract In this paper, we refine the method of Chowla and Erdős on the irrationality of Lambert series and study a necessary condition for the infinite series ∑ θ ( n ) / q n {\sum\theta(n)/q^{n}} to be a rational number, where q is an integer with | q | > 1 {|q|>1} and θ is an arithmetic function with suitable divisibility and growth conditions. As applications of our main theorem, we give linear independence results for various kinds of Lambert series.
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