Maass form twisted Shintani $\mathscr{L}$-functions

TL;DR

This paper introduces Maass-form twisted Shintani $\\mathscr{L}$-functions and explores their analytic properties, revealing insights into the distribution of shapes of cubic rings.

Contribution

It presents the definition and analysis of a new class of $\\mathscr{L}$-functions associated with Maass forms, linking them to cubic ring shape distributions.

Findings

Established analytic properties of the new $\\mathscr{L}$-functions

Connected the functions to the distribution of cubic ring shapes

Provided foundational results for further research in automorphic forms

Abstract

The Maass-form twisted Shintani $\mathscr{L}$-functions are introduced, and some of their analytic properties are studied. These functions contain data regarding the distribution of shapes of cubic rings.