Working with Dirichlet polynomials part2(Mathematics)
- Averages of long Dirichlet polynomials with modular coefficients(arXiv)
Author : Brian Conrey, Alessandro Fazzari
Abstract : We study the moments of L-functions associated with primitive cusp forms, in the weight aspect. In particular, we obtain an asymptotic formula for the twisted moments of a \textit{long} Dirichlet polynomial with modular coefficients. This result, which is conditional on the Generalized Lindelöf Hypothesis, agrees with the prediction of the recipe by Conrey, Farmer, Keating, Rubinstein and Snait
2. Approximations of Hecke-Maass L-functions by short Dirichlet polynomials(arXiv)
Author : Jiseong Kim
Abstract : By assuming the Ramanujan conjecture, we approximate L-functions associated to SL(3,Z) Hecke-Maass cusp forms (on average) by short Dirichlet polynomials. For the proof, we apply a variant of the Kuznetsov trace formula. As an application, we get some zero density estimates of SL(3,Z) Hecke-Maass cusp forms.
