Subconvexity of twisted Shintani zeta functions. (English) Zbl 07930587
Summary: Previously the authors proved subconvexity of Shintani’s zeta function enumerating class numbers of binary cubic forms. Here we return to prove subconvexity of the Maass form twisted version. The method demonstrated here has applications to the subconvexity of some of the twisted zeta functions introduced by F. Sato. The argument demonstrates that the symmetric space condition used by Sato is not necessary to estimate the zeta function in the critical strip.
MSC:
| 11M41 | Other Dirichlet series and zeta functions |
| 11N45 | Asymptotic results on counting functions for algebraic and topological structures |
| 11N64 | Other results on the distribution of values or the characterization of arithmetic functions |
| 11F12 | Automorphic forms, one variable |
| 11H06 | Lattices and convex bodies (number-theoretic aspects) |
| 11E45 | Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) |
| 12F05 | Algebraic field extensions |
| 43A85 | Harmonic analysis on homogeneous spaces |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
Keywords:
subconvexity; cubic ring; Maass form; space of lattices; zeta function; prehomogeneous vector space; oscillatory integralReferences:
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