Dirichlet characters and low-lying zeros of L-functions
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- Dirichlet characters and low-lying zeros of L-functions
- Cho, Perter J.; Park. Jeongho
- Issue Date
- Academic Press Inc.
- JOURNAL OF NUMBER THEORY, v.212, pp.203 - 232
- Let r be a positive integer ≥2. We consider a family of primitive Dirichlet characters of order r with conductor co-prime to r. For this family, we compute the one-level density with explicit lower order terms in two ways, using Weil's explicit formula and the Ratios conjecture. Also, the n-level density for the family twisted by a fixed cuspidal automorphic representation π of GLM(AQ) is obtained. It turns out that, when r≥3, the symmetry type for our family is always unitary.
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