Small first zeros of \(L\)-functions. (English) Zbl 1391.11110
Summary: From a family of \(L\)-functions with unitary symmetry, C. P. Hughes and Z. Rudnick [Q. J. Math. 54, No. 3, 309–333 (2003; Zbl 1068.11055)] obtained results on the height of its lowest zero. We extend their results to other families of \(L\)-functions according to the type of symmetry coming from statistics for low-lying zeros.
MSC:
| 11M41 | Other Dirichlet series and zeta functions |
| 11M50 | Relations with random matrices |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
Keywords:
\(L\)-function; density theorem; random matrix theory; smallest zero; differential equation with temporal shiftsCitations:
Zbl 1068.11055References:
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