On the zeros of linear combinations of \(L\)-functions of degree two on the critical line. Selberg's approach (Q2821887)
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scientific article; zbMATH DE number 6629500
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the zeros of linear combinations of \(L\)-functions of degree two on the critical line. Selberg's approach |
scientific article; zbMATH DE number 6629500 |
Statements
26 September 2016
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Riemann hypothesis
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zeros on the critical line
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Selberg class
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density theorems
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Hecke \(L\)-functions
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On the zeros of linear combinations of \(L\)-functions of degree two on the critical line. Selberg's approach (English)
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Define a linear combination of \(m\) distinct Hecke \(L\)-functions \(L_j(s)\) attached to complex characters on the ideal group, \(j=1,\dots,m\), by NEWLINE\[NEWLINEF(s)=\sum_{j=1}^{m}c_j L_j(s), \quad c_j \in \mathbb R. NEWLINE\]NEWLINENEWLINENEWLINEIn this paper, it is shown that on the interval \(\{s=\frac{1}{2}+it, T \leq t\leq 2T\}\), for the number of zeros \(N_0(T)\) of the function \(F(s)\), the following estimate holds NEWLINE\[NEWLINE N_0(T) \gg \frac{1}{m}T \log T. NEWLINE\]
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