Abstract
In this note, we present probabilisticlimit theorems on the complex plane as well as in functional spaces for the Lerch zeta-function with algebraic irrational parameter.
Highlights
We present probabilistic limit theorems on the complex plane as well as in functional spaces for the Lerch zeta-function with algebraic irrational parameter
}, and denote by the space of analytic on functions equipped with the topology of uniform convergence on compacta
We are in position to state a corrected joint limit theorem on the complex plane for Lerch zeta-functions
Summary
We present probabilistic limit theorems on the complex plane as well as in functional spaces for the Lerch zeta-function with algebraic irrational parameter. If α is algebraic irrational, J.W.S. Cassels [1] proved that at least 51 percent of elements of the set L(α) are linearly independent over the field of rational numbers Q. Denote by I (α) the maximal linearly independent over Q subset of L(α), and suppose that D(α) = L(α) \ I (α) = ∅.
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