اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBounds on shifted convolution sums for Hecke eigenforms
163
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Shifted convolution sums play a prominent role in analytic number theory. We investigate pointwise bounds, mean-square bounds, and average bounds for shifted convolution sums for Hecke eigenforms.
قيم البحث
اقرأ أيضاً
On a family of arithmetic hyperbolic 3-manifolds of squarefree level, we prove an upper bound for the sup-norm of Hecke-Maass cusp forms, with a power saving over the local geometric bound simultaneously in the Laplacian eigenvalue and the volume. By
a novel combination of diophantine and geometric arguments in a noncommutative setting, we obtain bounds as strong as the best corresponding results on arithmetic surfaces.
We investigate the equidistribution of Hecke eigenforms on sets that are shrinking towards infinity. We show that at scales finer than the Planck scale they do not equidistribute while at scales more coarse than the Planck scale they equidistribute o
n a full density subsequence of eigenforms. On a suitable set of test functions we compute the variance showing interesting transition behavior at half the Planck scale.
For a subset A of a finite abelian group G we define Sigma(A)={sum_{ain B}a:Bsubset A}. In the case that Sigma(A) has trivial stabiliser, one may deduce that the size of Sigma(A) is at least quadratic in |A|; the bound |Sigma(A)|>= |A|^{2}/64 has rec
ently been obtained by De Vos, Goddyn, Mohar and Samal. We improve this bound to the asymptotically best possible result |Sigma(A)|>= (1/4-o(1))|A|^{2}. We also study a related problem in which A is any subset of Z_{n} with all elements of A coprime to n; it has recently been shown, by Vu, that if such a set A has the property Sigma(A) is not Z_{n} then |A|=O(sqrt{n}). This bound was improved to |A|<= 8sqrt{n} by De Vos, Goddyn, Mohar and Samal, we further improve the bound to the asymptotically best possible result |A|<= (2+o(1))sqrt{n}.
In this work we provide a meromorphic continuation in three complex variables of two types of triple shifted convolution sums of Fourier coefficients of holomorphic cusp forms. The foundations of this construction are based in the continuation of the
spectral expansion of a special truncated Poincare series recently developed by Jeffrey Hoffstein. As a result we are able to produce previously unstudied and nontrivial asymptotics of truncated shifted sums which we expect to correspond to off-diagonal terms in the third moment of automorphic L-functions.
Let $f(n)$ be a multiplicative function with $|f(n)|leq 1, q$ be a prime number and $a$ be an integer with $(a, q)=1, chi$ be a non-principal Dirichlet character modulo $q$. Let $varepsilon$ be a sufficiently small positive constant, $A$ be a large c
onstant, $q^{frac12+varepsilon}ll Nll q^A$. In this paper, we shall prove that $$ sum_{nleq N}f(n)chi(n+a)ll Nfrac{loglog q}{log q} $$ and that $$ sum_{nleq N}f(n)chi(n+a_1)cdotschi(n+a_t)ll Nfrac{loglog q}{log q}, $$ where $tgeq 2, a_1, ldots, a_t$ are distinct integers modulo $q$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
