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pro vyhledávání: '"Getz, Jayce R."'
We count integral quaternion zeros of $\gamma_1^2 \pm \dots \pm \gamma_n^2$, giving an asymptotic when $n\ge 9$, and a likely near-optimal bound when $n=8$. To do so, we introduce a new, nonabelian delta symbol method, which is of independent interes
Externí odkaz:
http://arxiv.org/abs/2407.11804
Autor:
Getz, Jayce R.
We prove a Poisson summation formula for the zero locus of a quadratic form in an even number of variables with no assumption on the support of the functions involved. The key novelty in the formula is that all ``boundary terms'' are given either by
Externí odkaz:
http://arxiv.org/abs/2201.02583
Autor:
Choie, YoungJu, Getz, Jayce R.
The first author and Bump defined Schubert Eisenstein series by restricting the summation in a degenerate Eisenstein series to a particular Schubert variety. In the case of $\mathrm{GL}_3$ over $\mathbb{Q}$ they proved that these Schubert Eisenstein
Externí odkaz:
http://arxiv.org/abs/2107.01874
Braverman and Kazhdan proposed a conjecture, later refined by Ng\^o and broadened to the framework of spherical varieties by Sakellaridis, that asserts that affine spherical varieties admit Schwartz spaces, Fourier transforms, and Poisson summation f
Externí odkaz:
http://arxiv.org/abs/2103.10261
Autor:
Getz, Jayce R., Hsu, Chun-Hsien
Let $V_1,V_2,V_3$ be a triple of even dimensional vector spaces over a number field $F$ equipped with nondegenerate quadratic forms $\mathcal{Q}_1,\mathcal{Q}_2,\mathcal{Q}_3$, respectively. Let $ Y \subset \prod_{i=1}^3 V_i$ be the closed subscheme
Externí odkaz:
http://arxiv.org/abs/2009.11490
Autor:
Getz, Jayce R.
Let $\pi=\pi_1 \otimes \pi_2 \otimes \pi_3$ be a unitary cuspidal automorphic representation of $\mathrm{GL}_3^3(\mathbb{A}_F)$ where $F$ is a number field. Assume that $\pi$ is everywhere tempered. Under suitable local hypotheses, for a sufficiently
Externí odkaz:
http://arxiv.org/abs/1912.01405
Autor:
Getz, Jayce R., Liu, Baiying
Let $V_1,V_2,V_3$ be a triple of even dimensional vector spaces over a number field $F$ equipped with nondegenerate quadratic forms $\mathcal{Q}_1,\mathcal{Q}_2,\mathcal{Q}_3$, respectively. Let \begin{align*} Y \subset \prod_{i=1}V_i \end{align*} be
Externí odkaz:
http://arxiv.org/abs/1711.08087
Autor:
Getz, Jayce R., Liu, Baiying
Braverman and Kazhdan introduced influential conjectures generalizing the Fourier transform and the Poisson summation formula. Their conjectures should imply that quite general Langlands $L$-functions have meromorphic continuations and functional equ
Externí odkaz:
http://arxiv.org/abs/1707.06091
Autor:
Getz, Jayce R.
Publikováno v:
Journal of the Ramanujan Mathematical Society, Vol. 27, No. 2 (2012) 143-211
We present a collection of conjectural trace identities and explain why they are equivalent to base change and descent of automorphic representations of $\mathrm{GL}_n(\mathbb{A}_F)$ along nonsolvable extensions (under some simplifying hypotheses). T
Externí odkaz:
http://arxiv.org/abs/1701.01766
Autor:
Getz, Jayce R., Wambach, Eric
Publikováno v:
Amer. J. Math. 136 (2014), no.1, 1-58
We introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of Langlands et.al. (in the quadratic case) and the relative trace formula of Jacquet and Lai. Certain matching statements relating this twisted
Externí odkaz:
http://arxiv.org/abs/1701.01762