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Your search keyword '"Weak convergence"' showing total 2 results
2 results on '"Weak convergence"'

1. On universality in short intervals for zeta-functions of certain cusp forms.

Author

Laurinčikas, Antanas and Šiaučiūnas, Darius

Subjects
*LIMIT theorems, *ZETA functions, *MODULAR groups, *ANALYTIC functions, *ANALYTIC spaces, *MODULAR forms, *CUSP forms (Mathematics)
Abstract

In this paper, we consider universality in short intervals for the zeta-function attached to a normalized Hecke-eigen cusp form with respect to the modular group. For this, we apply a conjecture for the mean square in short interval on the critical strip for that zeta-function. The proof of the obtained universality theorem is based on a probabilistic limit theorem in the space of analytic functions. [ABSTRACT FROM AUTHOR]

Published
2024
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2. The Riemann hypothesis and universality of the Riemann zeta-function.

Author

Garunkštis, Ramūnas and Laurinčikas, Antanas

Subjects
*RIEMANN hypothesis, *ANALYTIC functions, *ZERO (The number), *ZETA functions, *MATHEMATICAL series
Abstract

We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts ζ(s + iγk), k ∈ ℕ, of the Riemann zeta-function, where γk are imaginary parts of nontrivial zeros of ζ(s). [ABSTRACT FROM AUTHOR]

Published
2018
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