اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Ramanujan-Petersson conjecture for Maass forms
155
0
0.0
(
0
)
تأليف
Andre Unterberger
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove the Ramanujan-Petersson conjecture for Maass forms of the group $SL(2,Z)$, with the help of automorphic distribution theory: this is an alternative to classical automorphic function theory, in which the plane takes the place usually ascribed to the hyperbolic half-plane.
قيم البحث
اقرأ أيضاً
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide audience of ma
thematicians---a mathematically rigorous instance of such a relation that emerged in recent years, showing a dynamical interpretation of certain Laplace eigenfunctions of hyperbolic surfaces.
We confirm the Hanna Neumann conjecture for topologically finitely generated closed subgroups $U$ and $W$ of a nonsolvable Demushkin group $G$. Namely, we show that begin{equation*} sum_{g in U backslash G/W} bar d(U cap gWg^{-1}) leq bar d(U) bar d(
W) end{equation*} where $bar d(K) = max{d(K) - 1, 0}$ and $d(K)$ is the least cardinality of a topological generating set for the group $K$.
As a consequence of the classification of finite simple groups, the classification of permutation groups of prime degree is complete, apart from the question of when the natural degree $(q^n-1)/(q-1)$ of ${rm PSL}_n(q)$ is prime. We present heuristic
arguments and computational evidence based on the Bateman-Horn Conjecture to support a conjecture that for each prime $nge 3$ there are infinitely many primes of this form, even if one restricts to prime values of $q$. Similar arguments and results apply to the parameters of the simple groups ${rm PSL}_n(q)$, ${rm PSU}_n(q)$ and ${rm PSp}_{2n}(q)$ which arise in the work of Dixon and Zalesskii on linear groups of prime degree.
In this paper, we explicitly construct harmonic Maass forms that map to the weight one theta series associated by Hecke to odd ray class group characters of real quadratic fields. From this construction, we give precise arithmetic information contain
ed in the Fourier coefficients of the holomorphic part of the harmonic Maass form, establishing the main part of a conjecture of the second author.
We introduce the notion of the automorphic dual of a matrix algebraic group defined over $Q$. This is the part of the unitary dual that corresponds to arithmetic spectrum. Basic functorial properties of this set are derived and used both to deduce ar
ithmetic vanishing theorems of ``Ramanujan type as well as to give a new construction of automorphic forms.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
