| Abstrakt: |
In this paper, we investigate the existence of large values of | L (s , χ) | , where χ varies over non-principal characters associated to prime polynomials Q over finite field 𝔽 q , as d (Q) → ∞ , and s ∈ (1 / 2 , 1 ]. When s = 1 , we provide a lower bound for the number of such characters. To do this, we adapt the resonance method to the function field setting. We also investigate this problem for | L (1 / 2 , χ) | , where now χ varies over even, non-principal, Dirichlet characters associated to prime polynomials Q over 𝔽 q , as d (Q) → ∞. In addition to resonance method, in this case, we use an adaptation of Gál-type sums estimate. [ABSTRACT FROM AUTHOR] |
