Modular forms on G 2 and their Standard L-Function

DOI10.1007/978-3-030-68506-5_12zbMath1490.11060arXiv1807.03884OpenAlexW2840162676MaRDI QIDQ4956867

Aaron Pollack

Publication date: 2 September 2021

Published in: Simons Symposia (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.03884

zbMATH Keywords

Fourier expansionmodular formsautomorphic form\(G_2\)Rankin-Selberg

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (1)

The completed standard \(L\)-function of modular forms on \(G_2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The embeddings of discrete series into principal series for an exceptional real simple Lie group of type \(G_2\)
• On cubic rings and quaternion rings
• Embeddings of discrete series into induced representations of semisimple Lie groups. II: Generalized Whittaker models for \(SU(2,2)\)
• On the standard \(L\)-function for \(G_ 2\)
• Fourier coefficients of Eisenstein series of the exceptional group of type \(G_2\)
• Generalized Whittaker vectors for holomorphic and quaternionic representations
• On the Rankin-Selberg integral of Kohnen and Skoruppa
• Lifting laws and arithmetic invariant theory
• Fourier coefficients of modular forms on \(G_2\).
• Whittaker functions for the large discrete series representations of \(\mathrm{SU}(2,1)\) and related zeta integrals
• The embeddings of discrete series into principal series for an exceptional real simple Lie group of type \(G_ 2\)
• The Fourier expansion of modular forms on quaternionic exceptional groups
• A \(\mathrm{G}_2\)-period of a Fourier coefficient of an Eisenstein series on \(\mathrm{E}_6\)
• On the Gelfand–Kirillov dimension of a discrete series representation
• The Rankin–Selberg integral with a non-unique model for the standard -function of
• A new way to get Euler products.
• On quaternionic discrete series representations, and their continuations.
• A Class of Supercuspidal Representations of G₂(k)
• Minimal representations of exceptional 𝑝-adic groups
• A Family of New-Way Integrals for the Standard ℒ-function of Cuspidal Representations of the Exceptional Group of TypeG₂
• Unramified Godement-Jacquet theory for the spin similitude group
• The spin -function on for Siegel modular forms
• On Dirichlet series whose coefficients are class numbers of integral binary cubic forms

This page was built for publication: Modular forms on G 2 and their Standard L-Function