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作者:Andrew Sutherland , David Zywina
来源:[J].Algebra & Number Theory(IF 0.625), 2017, Vol.11 (5), pp.1199-1229MSP
摘要:For each open subgroup $G$ of $\operatorname{GL}_2(\hat{\mathbb{Z}})$ containing $-I$with full determinant, let $X_G/\mathbb{Q}$ denote the modular curve thatloosely parametrizes elliptic curves whose Galois representation,which arises from the Galois action on its torsion points...
作者:Abhishek Saha
来源:[J].Algebra & Number Theory(IF 0.625), 2017, Vol.11 (5), pp.1009-1045MSP
摘要:Let $f$ be an $L^2$-normalized Hecke--Maass cuspidalnewform of level $N$, character $\chi$and Laplace eigenvalue $\lambda$. Let $N_1$ denote the smallestinteger such that $N|N_1^2$ and $N_0$ denote the largest integer suchthat $N_0^2 |N$. Let $M$ denote the conductor of $\chi$ an...
作者:Yuri Bilu , Florian Luca , David Masser
来源:[J].Algebra & Number Theory(IF 0.625), 2017, Vol.11 (5), pp.1047-1087MSP
摘要:\looseness=-1Andr\'e's celebrated theorem of 1998 implies that each complex straight line$Ax+By+C=0$ (apart from obvious exceptions) contains at most finitely manypoints $(j(\tau),j(\tau'))$, where $\tau,\tau'\in\mathbb H$ are algebraicof degree $2$. We show that there are only a...
作者:David Speyer
来源:[J].Algebra & Number Theory(IF 0.625), 2017, Vol.11 (5), pp.1231-1241MSP
摘要:We prove a number of conjectures due to Dinesh Thakur concerning sumsof the form $\sum_P h(P)$ where the sum is over monic irreduciblepolynomials $P$ in $\mathbb{F}_q[T]$, the function $h$ is a rationalfunction and the sum is considered in the $T^{-1}$-adic topology. As anexample...
作者:Jesse Thorner , Asif Zaman
来源:[J].Algebra & Number Theory(IF 0.625), 2017, Vol.11 (5), pp.1135-1197MSP
摘要:We prove an explicit version of Weiss' bound on the least norm of a primeideal in the Chebotarev density theorem, which is a significant improvement onthe work of Lagarias, Montgomery, and Odlyzko. As an application, we provethe first explicit, nontrivial, and unconditional upper...
作者:Dan Ciubotaru , Eric Opdam
来源:[J].Algebra & Number Theory(IF 0.625), 2017, Vol.11 (5), pp.1089-1134MSP
摘要:We give a new and independent parametrization ofthe set of discrete seriescharacters of an affine Hecke algebra$\mathcal{H}_{\mathbf{v}}$, in terms of a canonically definedbasis $\mathcal{B}_{\operatorname{gm}}$of a certainlattice of virtual elliptic characters of the underlying ...
作者:Shuichiro Takeda
来源:[J].Pacific Journal of Mathematics(IF 0.465), 2017, Vol.290 (1), pp.199-230MSP
摘要:We had previously constructed a metaplectic tensor product ofautomorphic representations of covers of $\operatorname{GL}_r$. To be precise, let$M=\operatorname{GL}_{\smash{r_1}}\times\cdots\times\operatorname{GL}_{\smash{r_k}}\subseteq\operatorname{GL}_r$ be a Levisubgroup of $\o...
作者:Joseph Grant , Robert Marsh
来源:[J].Pacific Journal of Mathematics(IF 0.465), 2017, Vol.290 (1), pp.77-116MSP
摘要:We describe presentations of braid groups of type $\mathit{ADE}$ and showhow thesepresentations are compatible with mutation of quivers.In types $A$ and $D$ these presentations can be understoodgeometrically using triangulated surfaces.We then give a categorical interpretation of...
作者:Shin Koizumi
来源:[J].Pacific Journal of Mathematics(IF 0.465), 2017, Vol.290 (1), pp.117-137MSP
摘要:We prove a Paley--Wiener theorem for the spectral projection ofsymmetric graphs and, as a corollary, derive a Paley--Wiener theoremfor the Helgason--Fourier transform. The proof is based on contourintegration arguments similar to those used to prove thePaley--Wiener theorem for E...
作者:Tim Weng Lee
来源:[J].Pacific Journal of Mathematics(IF 0.465), 2017, Vol.290 (1), pp.139-168MSP
摘要:For a connected reductive algebraic group $G$ over a numberfield$\Bbbk$, weinvestigate the Ryshkov domain $R_Q$ associatedto a maximal $\Bbbk$-parabolic subgroup $Q$ of $G$. By consideringthe arithmetic quotients $G(\Bbbk)\backslash G(\mathbb{A})^1/K$and $\Gamma_{\mkern-2mui}\bac...

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