Ha Huy Khoai, Vu Hoai An, Nguyen Duy Phuong: On value distribution of $L$-functions sharing finite sets with meromorphic functions, 265-280

Abstract:

In [17] the authors showed the existence of subsets $S\subset {\mathbb{C}}$ with 7 elements such that if a non-constant meromorphic function $f,$ having finitely many poles, and an $L$-function in the Selberg class share $S$ CM, then $f=L.$ In this paper, we present a class of such subsets $S$ with 5 elements. Moreover, when avoiding the hypothesis of having finitely many poles, we show a class of such subsets $S$ with $9$ elements.

Key Words: $L$-function, Selberg class, meromorphic function, unique range set.

2010 Mathematics Subject Classification: Primary 30D35; Secondary 11M06.

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