Uniqueness theorems of \(L\)-functions. (Chinese. English summary) Zbl 1424.11123
Summary: Using Nevanlinna theory, we study the uniqueness theorems of \(L\)-functions in the (extended) Selberg class and prove that there exist two sets \(S_1\) (including one or two elements) and \(S_2\) (including three elements) such that \(f \equiv L\) if \(E (S_i, f) = E (S_i, L)\) for \(i = 1, 2\).
MSC:
11M06 | \(\zeta (s)\) and \(L(s, \chi)\) |
30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |