Bombieri, E.; Perelli, A. Distinct zeros of \(L\)-functions. (English) Zbl 0891.11044 Acta Arith. 83, No. 3, 271-281 (1998). Let \(L_1(s)\) and \(L_2(s)\) be ‘independent’ \(L\)-functions, satisfying certain basic hypotheses akin to the Selberg Conjectures. Let \(m_j (\rho)\) \((j=1,2)\) be the multiplicity of \(\rho\) as a nontrivial zero of \(L_j(s)\), and set \[ D(T,L_1,L_2) =\sum_{0<\text{Im} \rho\leq T} \max \bigl(m_1 (\rho)- m_2(\rho), 0\bigr). \] Then, subject to the above hypotheses, it is shown that \(D(T,L_1, L_2)\gg T\log T\).In the case of Dirichlet \(L\)-functions, this was established by A. Fujii [Acta Arith. 28, 395-403 (1976; Zbl 0329.10028)]. However the present result includes \(GL_2\) \(L\)-functions, for example. The proof is motivated by the work of E. Bombieri and D. Hejhal [Duke Math. J. 80, 821-862 (1995; Zbl 0853.11074)]. Reviewer: D.R.Heath-Brown (Oxford) Cited in 2 ReviewsCited in 17 Documents MSC: 11M41 Other Dirichlet series and zeta functions 11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses Keywords:general \(L\)-functions; distinct zeros; \(GL_ 2\) \(L\)-functions Citations:Zbl 0329.10028; Zbl 0853.11074 PDFBibTeX XMLCite \textit{E. Bombieri} and \textit{A. Perelli}, Acta Arith. 83, No. 3, 271--281 (1998; Zbl 0891.11044) Full Text: DOI EuDML