Trees, quaternion algebras and modular curves
Mihran Papikian
研究了$\mathbb{F}_q(T)$上某些四元数代数的极大序模单位群在Bruhat-Tits树上的作用，并讨论了其在算术几何和群论中的应用.
We study the action on the Bruhat-Tits tree of unit groups of maximal orders in certain quaternion algebras over $\mathbb{F}_q(T)$ and discuss applications to arithmetic geometry and group theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Vector valued hermitian and quaternionic modular forms
推广文[FS 3]的方法，我们证明了向量值模形式的三个结构定理，其中两个对应于四维情形（两个厄米特模群，一个属于Eisenstein数域，另一个属于Gauss数域）.一个对应于6维情形（四元数模群）。
Genus two curves with quaternionic multiplication and modular jacobian
本文给出了一种确定带四元数乘法的模交换曲面$A_f$的所有主极化的同构类的方法，该模交换曲面带有一个不带复乘的规范化新形式$f$.我们包括一个例子，$A_f$与四元数乘法，我们发现数值曲线$C$的雅可比矩阵是$A_f$的数值逼近，我们证明了它有四元数乘法，是同源的$A_f$。
Which quaternion algebras act on a modular abelian variety?
设A是任意偶数维的\Q上的模阿贝尔簇.给出了全实数域上的四元数代数不成为A在\bar \Q上的自同态代数的判别准则.我们通过分析Gal（\bar \Q / \Q）在素数N处的A的N-挠在B中分支的点上的表示来完成这一点。
Siegel Modular Forms and Theta Series attached to quaternion algebras II
我们继续我们的研究吉田的提升，它与一对自守形式的adelic乘法群的四元数代数西格尔模形式的程度2。我们在这里考虑的情况下，自守形式的四元数代数对应于模形式的任意偶数重量和平方自由水平，特别是我们得到的西格尔模形式的重量3连接到一对椭圆模形式的重量2和4。
Elementary divisor theory for the modular group over quadratic field extensions and quaternion algebras
本文对二次域扩张和四元数代数上的幺模和模群给出了一个初等因子理论。特别是，我们调查哪些集合的初等因子可以发生。在一个附加的假设下，我们建立了一个对应的幺模和模双陪集。
We define a motive whose realizations afford modular forms (of arbitrary weight) on an indefinite division quaternion algebra. This generalizes work of Iovita--Spiess to odd weights in the spirit of Jordan--Livné. It also generalizes a construction of Scholl to indefinite division quaternion algebras.
Computations of algebraic modular forms associated with the definite quaternion algebra of discriminant $2$
本文提出一种计算判别式为$2$的定四元数代数极大序上代数模形式空间基的算法，构建了相应基的数据库，以支持代数模形式同余关系的研究。
Hecke algebras related to the unimodular and modular groups over hermitian fields and definite quaternion algebras
研究了与厄米域上的幺模群和模群有关的Hecke代数的结构以及确定的四元数代数。特别是，我们表明，在一般情况下，没有分解成主要成分。我们可以给出一组生成元，并在某些特殊情况下，我们推导出Siegel $Φ$ -算子的互换律。
Modular Heights of Quaternionic Shimura Curves
本文证明了一个公式，将全实数域上四元数 Shimura 曲线的模高表示为 Dedekind zeta 函数对数导数，基于 Yuan-Zhang-Zhang 和 Yuan-Zhang 的工作，受 Gross-Zagier 和 Kudla 纲领启发。
We use a combinatorial result relating the discriminant of the cycle pairing on a weighted finite graph to the eigenvalues of its Laplacian to deduce a formula for the orders of component groups of Jacobians of modular curves arising from quaternion algebras over $\mathbb{F}_q(T)$ or $\mathbb{Q}$. Our formula over $\mathbb{Q}$ recovers a result of Jordan and Livné.
Hecke structure of quaternionic modular forms mod $p$
本文建立了无限四元数代数上 Shimura 曲线模 p 模形式与确定四元数代数上代数模形式的 Hecke 特征值系统之间的双射，并显式构造了后者空间的 Hecke 结构，作为 Serre 致 Tate 信的四元数类比。
Associated graded modules for modular representations of quaternion algebras
针对Q_p有限非分歧扩域K上的非分裂四元数代数D，该文计算雅可比-朗兰兹对应中D^×预表示的对偶的相伴分次模。
Suppose that $G$ is a simple reductive group over $\mathbf{Q}$, with an exceptional Dynkin type, and with $G(\mathbf{R})$ quaternionic (in the sense of Gross-Wallach). In a previous paper, we gave an explicit form of the Fourier expansion of modular forms on $G$ along the unipotent radical of the Heisenberg parabolic. In this paper, we give the Fourier expansion of the minimal modular form $θ_{Gan}$ on quaternionic $E_8$, and some applications. The $Sym^{8}(V_2)$-valued automorphic function $θ_{Gan}$ is a weight four, level one modular form on $E_8$, which has been studied by Gan. The applicat…
For a totally real number field $F$ and a nonarchimedean prime $\mathfrak{p}$ of $F$ lying above a prime number $p$ we introduce certain sheaf cohomology groups that intertwine the $\mathfrak{p}^{\infty}$-tower of a quaternionic Hilbert modular variety associated to a quaternion algebra $D$ over $F$ that is split at $\mathfrak{p}$ and a $p$-adically admissible representation of $\mbox{PGL}_2(F_{\mathfrak{p}})$. Applied to infinitesimal $p$-adic deformations of the local factor at $\mathfrak{p}$ of a cuspidal automorphic representation $π$ of $D^*(\mathbb{A})$ this yields a natural construction…
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 notion of modular forms for $G$, anchored on the so-called quaternionic discrete series representations of $G(\mathbf{R})$. The purpose of this paper is to give an explicit form of the Fourier expansion of modular forms on $G$, along the unipotent radical $N$ of the Heisenberg parabolic $P = MN$ of $G$.
Flach system of Jacquet-Langlands type and quaternionic period
本文研究了模形式在定四元数代数上 Jacquet-Langlands 转移后的伴随 Selmer 群，证明其长度由四元数模形式的 Petersson 范数赋值给出，并基于 Flach 的 Euler 系统论证提出了一种不依赖 Siegel 模单位的新构造方法。
On $p$-adic quaternionic Eisenstein series
我们证明了，某些$p$ -adic爱森斯坦系列的四元数模群的程度2成为“真正的”模形式的水平$p$在几乎所有的情况下。为了证明这一点，我们引入了一个$U(p)$型算子。我们还表明，存在一个$p$ -adic爱森斯坦级数的上述类型，具有超越系数。Siegel和Hermitian模群的$p$ -adic Eisenstein级数的先前例子都是有理的（即，代数）。
Galois Representations with Quaternion Multiplications Associated to Noncongruence Modular Forms
本文研究了四次Scholl表示的相容族$ρ_{\ell}$，它对应于一个四次域$K$上的权为$κ> 2$的非同余尖点形式满足四元数乘法的空间$S$.证明了当$K$是全实的或$κ$是奇的时，$ρ_\ell$是自守的，即它的L-函数与$GL_4(\mathbb Q)$的自守形式的L-函数具有相同的Euler因子.进一步，通过三项Atkin和Swinnerton-Dyer同余，得到了$S$中非同余尖点形式的傅里叶系数与某些自守形式的Fourier系数之间的关系.
Let $D$ be a definite quaternion algebra over $\mathbb{Q}$ and $\mathcal{O}$ an Eichler order in $D$ of square-free level. We study distribution of the toric periods of algebraic modular forms of level $\mathcal{O}$. We focus on two problems: non-vanishing and sign changes. Firstly, under certain conditions on $\mathcal{O}$, we prove the non-vanishing of the toric periods for positive proportion of imaginary quadratic fields. This improves the known lower bounds toward Goldfeld's conjecture in some cases and provides evidence for similar non-vanishing conjectures for central values of twisted …
We present an explicit basis for orders of arbitrary level N>1 in definite rational quaternion algebras. These orders have applications to computations of spaces of elliptic and quaternionic modular forms.
Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At first: Every irreducible cuspidal representation of G is induced from a cuspidal type, i.e. from a certain irreducible representation of a compact open subgroup of G, constructed from a beta-extension and a cuspidal representation of a finite group. Secondly we show that two intertwining cuspidal types of G are up to equivalence conjugate under some element of G.
Automatic convergence and arithmeticity of modular forms on exceptional groups
本研究证明F₄与Eₙ型群上尖点四元数模形式空间具纯代数刻画，核心是证明相关无穷和绝对收敛，进而推出其存在傅里叶系数全为代数数的基，推动了例外群上模形式的算术性质研究。
In this article, using methods from geometric analysis and theory of heat kernels, we derive qualitative estimates of automorphic cusp forms defined over quaternion algebras. Using which, we prove an average version of the holomorphic QUE conjecture. We then derive quantitative estimates of classical Hilbert modular cusp forms. This is a generalization of the results from [3] and [9] to higher dimensions.
We study arithmetic intersections on twisted (quaternionic) Hilbert modular surfaces and Shimura curves over a real quadratic field. Our first main result is the determination of the degree of the top arithmetic Todd class of an arithmetic twisted Hilbert modular surface. This quantity is then related to the arithmetic volume of a Shimura curve, via the arithmetic Grothendieck-Riemann-Roch theorem and the Jacquet-Langlands correspondence.
Counting Discrete, Level-$1$, Quaternionic Automorphic Representations on $G_2$
本文利用“hyperendoscopy”技术发展一般迹公式，研究例外群 $G_2$ 上的四元数自守表示，克服了离散级数非正则的技术困难，并计算出 level-$1$ 表示空间的维数。
We develop a theory of modular forms on the groups $\mathrm{SO}(3,n+1)$, $n \geq 3$. This is very similar to, but simpler, than the notion of modular forms on quaternionic exceptional groups, which was initiated by Gross-Wallach and Gan-Gross-Savin. We prove the results analogous to those of earlier papers of the author on modular forms on exceptional groups, except now in the familiar setting of classical groups. Moreover, in the setting of $\mathrm{SO}(3,n+1)$, there is a family of absolutely convergent Eisenstein series, which are modular forms. We prove that these Eisenstein series have al…
Automatic convergence for holomorphic modular forms
本文研究了解析模形式在管域上的自动收敛性，涵盖了正交群、辛群、单位ary群和四元单位ary群以及例外群E_7的案例。
Computing quaternionic representations via twisted forms of Bruhat-Tits trees
通过扭曲形式的布鲁哈-蒂茨树研究四元数代数的有限子群表示，计算积分形式集的大小。
Quaternion algebras, Heegner points and the arithmetic of Hida families
给定一个新的形式f，我们扩展霍华德的结果的变化Heegner点在Hida家庭的f到一般的四元数设置。更准确地说，我们建立大Heegner点和大Heegner类的兼容家庭的Heegner点的塔志村曲线。我们的方法，系统地利用最优嵌入理论的新颖性，包括在治疗的情况下，确定四元数代数和不定四元数代数的情况下，在一个统一的方式。我们证明结果的大小Nekovásness的扩展Selmer群附加到适当的大伽罗瓦表示，我们制定两个变量岩泽主要的拓扑结构在确定的情况下，在不确定的情况下。此外，在定解情形下，我们给出了关于f的Hida族中与f同枝的模形式的L-函数（的转折）在临界点消失的精化定理。
On bi-periodic Padovan and Perrin quaternions over finite fields
本文研究了有限域上双周期Padovan和Perrin四元数的结构关系及范数属性，并推导出零因子和可逆元的显式准则。
$S$-arithmetic groups acting simply transitively on products of Bruhat-Tits trees
针对全定四元数代数上的Bruhat-Tits树，利用Kirschmer和Voight的分类，构造了几乎对所有素理想简单传递作用的同余算术格，并推广到树的乘积，产生新的Ramanujan Cayley图与立方复形。
We determine the quantum variance of a sequence of families of automorphic forms on a compact quotient arising from a non-split quaternion algebra. Our results compare to those obtained by Luo--Sarnak, Zhao, and Sarnak--Zhao on the modular curve, whose method required a cusp. Our method uses the theta correspondence to reduce the problem to the estimation of metaplectic Rankin--Selberg convolutions. We apply it here to the first non-split case.
Local diophantine properties of modular curves of $\cal{D}$-elliptic sheaves
研究了局部域上$\cal{D}$ -椭圆层的模曲线上有理点的存在性及其特殊纤维的结构.讨论了它的一些应用，包括寻找由四元数代数产生的算术群的表示，寻找$\cal{D}$ -椭圆层的模曲线的方程，以及构造违反Hasse原理的曲线.
We apply the theory of Bruhat-Tits trees to the study of optimal embeddings of two and three dimensional commutative orders into quaternion algebras. Specifically, we determine how many conjugacy classes of global Eichler orders in a quaternion algebra yield optimal representations of such orders. This completes the previous work by C. Maclachlan, who considered only Eichler orders of square free level and integral domains as sub-orders. The same technique is used in the second part of this work to compute local embedding numbers, extending previous results by J. Brzezinski.
Serre weights for quaternion algebras
本文研究了F的绝对伽罗瓦群的不可约二维模p表示的可能权，F是全实数域，在这个意义上它是模的，即它来自以F为中心的定四元数代数上的一个自守形式，该代数在除p的所有地方都是分歧的.在大多数情况下，我们确定可能的权重的精确列表;在其余情况下，我们确定可能的权重，直到一个简短而明确的例外列表。
This article has three goals. First, we generalize the result of Deuring and Serre on the characterization of supersingular locus of modular curves to all Shimura varieties given by totally indefinite quaternion algebras over totally real number fields. Second, we generalize the result of Ribet on arithmetic level raising to such Shimura varieties in the inert case. Third, as an application to number theory, we use the previous results to study the Selmer group of certain triple product motive of an elliptic curve, in the context of the Bloch--Kato conjecture.
Modular embeddings and automorphic Higgs bundles
我们研究半算术富克斯群的模嵌入。首先，我们证明了一些纯粹的代数几何，甚至拓扑标准的正则映射从光滑的复曲线到四元数志村品种覆盖的模嵌入。然后我们建立了模嵌入的一个抽象形式，并应用我们的准则研究了$\mathbb{C}$的抽象域自同构对模嵌入的影响。最后，通过重言式置换定义理想，得到了$\mathbb{Q}$的绝对伽罗瓦群作用于由（算术或非算术）三角形群的主同余子群定义的dessins d'enfants.
Cohomological interpretation of quadratic modular symbols
Bayer和Blanco-Chacón最近定义了判别式D的不定四元数有理代数的N级Eichler阶上的Shimura曲线X（D，N）的二次模符号.在本文中，我们给出了这些二次模符号的上同调解释。还提供了一些志村曲线的同调的显式计算。
We explore a natural action of Hecke operators acting on formal sums of optimal embeddings of real quadratic orders into Eichler orders. By associating an optimal embedding to its root geodesic on the corresponding Shimura curve, we can consider the signed intersection number of pairs of embeddings. Using the Hecke operators and the intersection pairing, we construct a generating series that is demonstrated to be a classical modular form of weight two.
We show that the completed Hecke algebra of $p$-adic modular forms is isomorphic to the completed Hecke algebra of continuous $p$-adic automorphic forms for the units of the quaternion algebra ramified at $p$ and $\infty$. This gives an affirmative answer to a question posed by Serre in a 1987 letter to Tate. The proof is geometric, and lifts a mod $p$ argument due to Serre: we evaluate modular forms by identifying a quaternionic double-coset with a fiber of the Hodge-Tate period map, and extend functions off of the double-coset using fake Hasse invariants. In particular, this gives a new proo…
Computing quaternion quotient graphs via representation of orders
研究了整体函数域上一般线性群的局部Bruhat-Tits树的商顶点与某些四元数代数的极大序模共轭类的对应关系.如果商图是已知的，则商图和阶之间的相互作用可以用来研究阶的表示，反之亦然。利用这一逆定理，我们找到了不同位置上的商图之间的一个互反律，该互反律足以递归地计算有理函数域上矩阵代数的所有局部商图.
Artin characters, Hurwitz trees and the lifting problem
研究了$p$ -adic开圆盘的自同构有限群.特别地，我们将Green，Matignon和Henrio的结果从$p$阶循环群推广到任意有限群.作为应用，我们产生了一个反例的Chinburg，Guralnick和Harbater的问题，关于广义四元数群的局部提升问题。
We derive explicit isomorphisms between certain congruence subgroups of the Siegel modular group, the Hermitian modular group over an arbitrary imaginary-quadratic number field and the modular group over the Hurwitz quaternions of degree 2 and the discriminant kernels of special orthogonal groups SO 0 (2, n), n = 3, 4, 6. The proof is based on an application of linear algebra adapted to the number theoretical needs.
A classification of $\mathbb C$-Fuchsian subgroups of Picard modular groups
给定$\mathbb Q$的一个虚二次扩张$K$，给出了复双曲平面$\mathbb H^2_\mathbb C$中Picard模群$\operatorname{PSU}_{1,2}(\mathcal O_K)$的保复测地线的极大非初等子群的分类.作为对Holzapfel，Chinburg-Stover和Möller-Toledo工作的补充，我们证明了这些最大$\mathbb C$ -Fuchsian子群是算术的，它们是由四元数代数$\Big(\!\begin{array}{c} D\,,D_K\\\hline\mathbb QQ\end{array} \!\Big)$对某些显式$D\in\mathbb N-\{0\}$和$D_K$ $K$的判别式产生的.从而证明了在$\mathbb P_2(\mathbb C)$的超球面中存在无穷多个$K$ -算术链轨道.
Towards an analogue of Ihara's lemma for Shimura curves
这项工作的目的是目前的一个开放的问题的艺术现状：提供一个类似的志村曲线的Ihara的引理\cite{Ihara73}，其中持有模曲线。我们将描述我们的直接结果对“问题的Ihara”，我们将提出一些可能的方法，给我们的猜想在四元数代数的同余子群问题的制定。由于某些模形式可以被重新解释为Shimura曲线的上同调的元素，我们将描述关于模形式的同余模的“Ihara问题”的一个推论和关于提高模形式的水平问题的一个推论。
Spherical designs for finite quaternionic unit groups and their applications to modular forms
本文确定三个有限单位四元数群 2T、2O、2I 的调和强度，证明其作为球面设计的极小唯一性，并利用该刻画在不依赖模形式理论的情况下确定相关球面 theta 函数张成空间维数为零的情形。
Presentations for quaternionic $S$-unit groups
本文的目的是给出有理域$\mathbb{Q}$上Hamilton四元数中Hurwitz阶射影$S$ -单位群的表示.据我们所知，这提供了一个$S$ -算术格在一个半单李群与$S$大的第一个明确的介绍。特别是，我们给介绍了集团的产品上的Bruhat-山雀树的作用不可约和cocompanies。我们还包括一些讨论和实验相关的同余子群问题，这是开放的，当$S$包含至少两个奇素数。在附录中，我们提供了代码，允许读者计算任意有限集$S$的表示。
Quantum variance on quaternion algebras, III
本文利用余伴随轨道方法的解析形式，解决了紧算术双曲曲面上Hecke–Maass尖点形式微局部提升的渐近量子方差问题，推广了非紧模曲面情形。
We define a notion of modular forms of half-integral weight on the quaternionic exceptional groups. We prove that they have a well-behaved notion of Fourier coefficients, which are complex numbers defined up to multiplication by $\pm 1$. We analyze the minimal modular form $Θ_{F_4}$ on the double cover of $F_4$, following Loke--Savin and Ginzburg. Using $Θ_{F_4}$, we define a modular form of weight $\frac{1}{2}$ on (the double cover of) $G_2$. We prove that the Fourier coefficients of this modular form on $G_2$ see the $2$-torsion in the narrow class groups of totally real cubic fields.
Applications of patching the coherent cohomology of modular curves
本文应用Taylor-Wiles-Kisin补丁方法研究模曲线的相干上同调最小级，通过q展开原理建立补丁模块的乘法一性，并证明晶格变形环的部分规范化的Cohen-Macaulay性，进一步得出晶格点在特征p下的Zariski稠密性及Serre模p四元数模形式的乘法一性结果。
The stabilizers in a Drinfeld modular group of the vertices of its Bruhat-Tits tree: an elementary approach
设$K$是一个具有常数域$k$的单变量代数函数域，$C$是由$K$中所有在$K$的一个固定位置$\infty$之外积分的元素组成的Dedekind整环.当$k$是有限的组$GL_2(C)$起着核心作用的理论德林费尔德模曲线类似所发挥的$SL_2(Z)$在经典理论的模块形式。当$k$是有限的（分别为无穷大），我们将群$GL_2(C)$称为算术（分别非算术）Drinfeld模群。与$GL_2(C)$相关的是其Bruhat-Tits树，$T$。群的结构是从商图$GL_2(C)\backslash T$的结构导出的。使用一个初等的方法，这是指明确的矩阵，我们确定的结构的所有顶点稳定的$T$。这推广了Serre，Takahashi和作者的结果.我们还确定了$GL_2(C)\backslash T$的顶点的所有可能的化合价的重要特殊情况下，$\infty$度为1。
A Gross-Zagier formula for quaternion algebras over totally real fields
我们证明了Gross和Zagier关于奇异模差因式分解定理的高维推广。给出了椭圆曲线与两个不同的虚二次域$K$和$K^\prime$的复乘的同构数的计数公式，证明了这一结果.等价地，Gross-Zagier公式计算虚二次域的整数环在$B_{p, \infty}$中的最优嵌入，$B_{p, \infty}$是$\QQ$上的定四元数代数，仅在$p$和无穷远处分支。本文给出了严格类数为1的全实数域上的定四元数代数中本原CM域的整数环同时嵌入超特殊阶的个数的一个类似的计数公式。我们的结果也可以看作是不同域上具有CM的阿贝尔簇之间模$\frak{p} | p$同构个数的一个计数公式。我们的计数公式也可以用来确定哪些超特殊素数出现在与两个不同CM域相关联的CM点上的Siegel模函数的值的差的因式分解中，并给出这些超奇异素数可能出现的界。在亏格2曲线的雅可比行列式的特殊情况下，这提供了关于Igusa不变量的分子的因子分解的信息，因此也与构造用于密码学的亏格2曲线的问题有关。
We extend our previous computations for the relative positions of branches of quaternions to the case of local fields of even characteristic. This is a key step to understand the set of maximal orders containing a given suborder, which is useful, for instance, to compute relative spinor images, thus solving the selectivity problem. In our previous work, the results where given in terms of the quadratic defect. In the present context, we introduce and characterize an analogous concept for Artin-Schreier extensions. It is no longer useful to restrict our attention to orders generated by pure qua…
Let $A$ be a quaternion algebra over a number field $F$, and $\mathcal{O}$ be an $O_F$-order of full rank in $A$. Let $K$ be a quadratic field extension of $F$ that embeds into $A$, and $B$ be an $O_F$-order in $K$. Suppose that $\mathcal{O}$ is a Bass order that is well-behaved at all the dyadic primes of $F$. We provide a necessary and sufficient condition for $B$ to be optimally spinor selective for the genus of $\mathcal{O}$. This partially generalizes previous results on optimal (spinor) selectivity by C. Maclachlan [Optimal embeddings in quaternion algebras. J. Number Theory, 128(10):285…
Modular realizations of hyperbolic Weyl groups
研究了最近发现的双曲外尔群与陌生的模群之间的同构。这些模群定义在赋范可除代数的整数域上，我们重点讨论涉及四元数和八元数的情形。我们概述了如何构建和分析这些群体的自守形式，它们的结构取决于整数域的基本算术性质。利用单位八维数及其自同构群给出了外尔群W（E ~ 8）的一种新的实现.
Modular elliptic curves and hyperbolic uniformization
研究将椭圆曲线双曲均匀化概念从有理数域扩展到奇数次完全实域，利用志村曲线，证明算术型双曲均匀化的存在意味着几何模性。
On computing quaternion quotient graphs for function fields
设$Λ$是$\mathbb{F}_q(T)$上可除四元数代数中在位置$\infty$分裂的极大$\mathbb{F}_q[T]$ -阶.本文给出了一个计算单位群$Λ^*$在与$PGL_2(\mathbb{F}_q((1/T)))$相关的Bruhat-Tits树$\mathcal{T}$上作用的基本区的算法。这个作用是上半平面上的一个余紧Fuchsian群的作用的函数场模拟。该算法还产生一个显式的介绍组$Λ^*$的发电机和关系。此外，我们确定了一个上限，其运行时间使用$Λ^*\backslash\mathcal{T}$是{ \em几乎} Ramanujan。
Computing fundamental domains for the Bruhat-Tits tree for GL2(Qp), p-adic automorphic forms, and the canonical embedding of Shimura curves
我们描述了一个算法，用于计算某些四元数的Bruhat-Tits树GL 2（QP）。作为应用，我们描述了一个算法，以获得（几何）方程的正则嵌入的志村曲线。
A Fourier-Jacobi Dirichlet series attached to modular forms of $SO(2,4)$
本文研究了与 $SO(2,4)$ 模形式相关的傅里叶-雅可比狄利克雷级数，并证明其与标准 $L$-函数的关系。
A classification of $\mathbb R$-Fuchsian subgroups of Picard modular groups
本研究对虚二次域上Picard模群中保持复双曲平面内全实全测地平面的极大非初等$\u211d$-Fuchs子群进行分类，证明其算术性并明确其来源的四元数代数，得出复射影平面超球面中存在无穷多$K$-算术$\u211d$-圆轨道的结论。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。