Corpus ID: 235458030

Counting Discrete, Level-$1$, Quaternionic Automorphic Representations on $G_2$

@inproceedings{Dalal2021CountingDL,
  title={Counting Discrete, Level-\$1\$, Quaternionic Automorphic Representations on \$G\_2\$},
  author={Rahul Dalal},
  year={2021}
}
Quaternionic automorphic representations are one attempt to generalize to other groups the special place holomorphic modular forms have among automorphic representations of GL2. Here, we study quaternionic automorphic representations on the exceptional group G2. Using “hyperendoscopy” techniques from a previous work, we develop for quaternionic, G2representations an analog of the Eichler-Selberg trace formula for classical modular forms. We then use this together with some techniques of… Expand

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SHOWING 1-10 OF 32 REFERENCES
Eisenstein series and automorphic representations
We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly widerExpand
Level one algebraic cusp forms of classical groups of small ranks
We determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GL_n over Q of any given infinitesimal character, for essentially all n <= 8. For this, weExpand
Dimensions of spaces of level one automorphic forms for split classical groups using the trace formula
We consider the problem of explicitly computing dimensions of spaces of automorphic or modular forms in level one, for a split classical group $\mathbf{G}$ over $\mathbb{Q}$ such thatExpand
On the Euler characteristic of the discrete spectrum
Abstract This paper, which is largely expository in nature, seeks to illustrate some of the advances that have been made on the trace formula in the past 15 years. We review the basic theory of theExpand
The Fourier expansion of modular forms on quaternionic exceptional groups
Suppose that $G$ is a simple adjoint reductive group over $\mathbf{Q}$, with an exceptional Dynkin type, and with $G(\mathbf{R})$ quaternionic (in the sense of Gross-Wallach). Then there is a notionExpand
Modular forms on G 2 and their Standard L-Function
The purpose of this partly expository paper is to give an introduction to modular forms on $G_2$. We do this by focusing on two aspects of $G_2$ modular forms. First, we discuss the Fourier expansionExpand
On quaternionic discrete series representations, and their continuations.
Among the discrete series representations of a real reductive group G, the simplest family to study are the holomorphic discrete series. These representations exist when the Symmetrie space G/ K hasExpand
On the stabilization of the trace formula.
This is the first volume of a projected series of two or three collections of mainly expository articles on the arithmetic theory of automorphic forms. The books are intended primarily for two groupsExpand
Multiplicity of Eisenstein series in cohomology and applications to $GSp_4$ and $G_2$
We set up a general framework to compute the exact multiplicity with which certain automorphic representations appear in both the cuspidal and Eisenstein cohomology of locally symmetric spaces. WeExpand
Sato–Tate theorem for families and low-lying zeros of automorphic $$L$$L-functions
We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let $$G$$G be a reductive group over a number field $$F$$FExpand
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