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arXiv · 1604.04396

Joint universality for dependent $L$-functions

Łukasz Pańkowski
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Abstract

We prove that, for arbitrary Dirichlet $L$-functions $L(s;χ_1),\ldots,L(s;χ_n)$ (including the case when $χ_j$ is equivalent to $χ_l$ for $j\ne k$), suitable shifts of type $L(s+iα_jt^{a_j}\log^{b_j}t;χ_j)$ can simultaneously approximate any given analytic functions on a simply connected compact subset of the right open half of the critical strip, provided the pairs $(a_j,b_j)$ are distinct and satisfy certain conditions. Moreover, we consider a discrete analogue of this problem where $t$ runs over the set of positive integers.

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Łukasz Pańkowski. 2016-04-15. Joint universality for dependent $L$-functions. https://doi.org/10.1007/s1113

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