First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters

Abstract

We evaluate asymptotically the smoothed first moment of central values of families of primitive cubic, quartic and sextic Dirichlet $L$-functions, using the method of double Dirichlet series. Quantitative non-vanishing result for these $L$-values are also proved.

11 pages. arXiv admin note: text overlap with arXiv:2306.10726

References in corpus (1)

• Moments of central values of quartic Dirichlet $L$-functions