1. "Almost" universality of the Lerch zeta-function.
- Author
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LAURINČIKAS, ANTANAS
- Subjects
- *
ZETA functions , *ANALYTIC functions , *DELUSIONS , *PROBABILITY theory , *ALGEBRA - Abstract
The Lerch zeta-function L(λ, α, s) with a transcendental parameter α, or with rational parameters α and λ is universal, i.e., a wide class of analytic functions is approximated by shifts L(λ, α, s + iτ), τ ∈ R. The case of an algebraic irrational α is an open problem. In the paper, it is proved that for all parameters α, 0 < α < 1, and λ, 0 < λ 6 1, including an algebraic irrational α, there exists a closed non-empty set of analytic functions Fα,λ such that every function f ∈ Fα,λ can be approximated by shifts L(λ, α, s + iτ). [ABSTRACT FROM AUTHOR]
- Published
- 2019