Abstract
Let \(P(z)\) be a polynomial of degree \(q\) without multiple zeros, let \(S\) be the zero set of \(P(z)\), and let \(k\) be the number of distinct roots of the derivative of \(P\). Assume that \(P(z)\) is a strong uniqueness polynomial for \(L\)-functions in the Selberg class. We prove that two \(L\)-functions \(L_1\) and \(L_2\) in the Selberg class sharing \(S\) with multiplicity \(\leq m\) (i. e. \(E_{L_1,m)}(S)=E_{L_2,m)}(S))\) necessarily coincide if one of the following conditions holds: (i) \(m=1\) and \(q\geq 2k+5\); (ii) \(2\leq m<\infty\) and \(q\geq 2k+3\).
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Khoai, H.H., An, V.H. & Hoa, P.N. Truncated Sharing of Subsets and Uniqueness of \(L\)-Functions in the Extended Selberg Class. Math Notes 113, 191–199 (2023). https://doi.org/10.1134/S0001434623010224
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DOI: https://doi.org/10.1134/S0001434623010224