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pro vyhledávání: '"Emory, Melissa"'
Let $\GSpin(V)$ (resp. $\GPin(V)$) be a general spin group (resp. a general Pin group) associated with a nondegenerate quadratic space $V$ of dimension $n$ over an Archimedean local field $F$. For a nondegenerate quadratic space $W$ of dimension $n-1
Externí odkaz:
http://arxiv.org/abs/2409.09320
In the early 2000's, R. Langlands proposed a strategy called Beyond Endoscopy to attack the principle of functoriality, which is one of the central questions of present day mathematics. A first step was achieved by A. Altug who worked with the group
Externí odkaz:
http://arxiv.org/abs/2404.10139
Autor:
Emory, Melissa, Goodson, Heidi
We consider the curves $ y^2=x^{2^m} -c$ and $y^2=x^{2^{d}+1}-cx$ over the rationals where $c \in \mathbb{Q}^{\times}.$ These curves are related via their associated Jacobian varieties in that the Jacobians of the latter appear as factors of the Jaco
Externí odkaz:
http://arxiv.org/abs/2401.06208
Autor:
Emory, Melissa, Takeda, Shuichiro
Each orthogonal group $\OO(n)$ has a nontrivial $\GL(1)$-extension, which we call $\GPin(n)$. The identity component of $\GPin(n)$ is the more familiar $\GSpin(n)$, the general Spin group. We prove that the restriction to $\GPin(n-1)$ of an irreducib
Externí odkaz:
http://arxiv.org/abs/2104.04814
Autor:
Emory, Melissa, Goodson, Heidi
We determine the Sato-Tate groups and prove the generalized Sato-Tate conjecture for the Jacobians of curves of the form $$ y^2=x^p-1 \text{ and } y^2=x^{2p}-1,$$ where $p$ is an odd prime. Our results rely on the fact the Jacobians of these curves a
Externí odkaz:
http://arxiv.org/abs/2004.10583
Autor:
Emory, Melissa
Publikováno v:
Pacific J. Math. 306 (2020) 115-151
We formulate a global Gan-Gross-Prasad conjecture for general spin groups. That is, we formulate a conjecture on a relation between periods of certain automorphic forms on $GSpin_{n+1} \times GSpin_n$ along the diagonal subgroup $GSpin_n$ and some $L
Externí odkaz:
http://arxiv.org/abs/1901.01746
Publikováno v:
International Journal of Number Theory, Volume No. 17, Issue No. 10, pp. 2175 - 2206, Year 2021
We consider the identity component of the Sato-Tate group of the Jacobian of curves of the form $$C_1\colon y^2=x^{2g+2}+c, C_2\colon y^2=x^{2g+1}+cx, C_3\colon y^2=x^{2g+1} +c,$$ where $g$ is the genus of the curve and $c\in\mathbb Q^*$ is constant.
Externí odkaz:
http://arxiv.org/abs/1812.00242
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