The cubic Pell equation $L$-function

DOI10.4064/aa220918-18-8arXiv2209.11874OpenAlexW4387146692MaRDI QIDQ6071862

Gerhardt Hinkle, Dorian Goldfeld

Publication date: 29 November 2023

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.11874

zbMATH Keywords

cubic theta functionPicard hypergeometric functioncubic Pell equationTakhtajan-Vinogradov trace formula

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Cubic and quartic Diophantine equations (11D25)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The arithmetic and geometry of some hyperbolic three manifolds
• On Maass wave forms and the imaginary quadratic Doi-Naganuma lifting
• Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. (On a new type of nonanalytic automorphic functions and the determination of Dirichlet series by functional equations)
• A cubic analogue of the theta series.
• A cubic analogue of the theta series. II.
• Imprimitive Gaussian Sums and Theta Functions Over a Number Field
• Mean value estimates for exponential sums and L-functions: a spectral theoretic approach.
• An orthogonality relation for (with an appendix by Bingrong Huang)
• LOW‐LYING ZEROS OF L ‐FUNCTIONS FOR MAASS FORMS OVER IMAGINARY QUADRATIC FIELDS
• Bounds and algorithms for the -Bessel function of imaginary order
• Low lying zeros of families of \(L\)-functions
• Non‐vanishing of symmetric cube L$L$‐functions

This page was built for publication: The cubic Pell equation $L$-function