Non-vanishing of Maass form 𝐿-functions of cubic level at the central point

Abstract With the method of mollification and the simple Kuznetsov trace formula, we study the central 𝐿-values of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>GL</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> \mathrm{GL}_{2} Maass forms of cubic level and establish a positive-proportional non-vanishing result in the spectral aspect in short intervals.