Transition mean values of shifted convolution sums

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The spectral decomposition of shifted convolution sums

Let π1, π2 be cuspidal automorphic representations of PGL2(R) of conductor 1 and Hecke eigenvalues λπ1,2 (n), and let h > 0 be an integer. For any smooth compactly supported weight functions W1,2 : R → C and any Y > 0 a spectral decomposition of the shifted convolution sum

متن کامل

Shifted Convolution Sums Involving Theta Series

Let f be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by λf (n) its n-th Hecke eigenvalue. Let r(n) = # { (n1, n2) ∈ Z : n21 + n22 = n } . In this paper, we study the shifted convolution sum Sh(X) = ∑ n≤X λf (n+ h)r(n), 1 ≤ h ≤ X, and establish uniform bounds with respect to the shift h for Sh(X).

متن کامل

Special values of shifted convolution Dirichlet series

In a recent important paper, Hoffstein and Hulse [14] generalized the notion of Rankin-Selberg convolution L-functions by defining shifted convolution L-functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.

متن کامل

Asymptotic bounds for special values of shifted convolution Dirichlet series

In [15], Hoffstein and Hulse defined the shifted convolution series of two cusp forms by “shifting” the usual Rankin-Selberg convolution L-series by a parameter h. We use the theory of harmonic Maass forms to study the behavior in h-aspect of certain values of these series and prove a polynomial bound as h → ∞. Our method relies on a result of Mertens and Ono [22], who showed that these values ...

متن کامل

Convolution Sums of Some Functions on Divisors

One of the main goals in this paper is to establish convolution sums of functions for the divisor sums σ̃s(n) = ∑ d|n(−1)d and σ̂s(n) = ∑ d|n(−1) n d d, for certain s, which were first defined by Glaisher. We first introduce three functions P(q), E(q), and Q(q) related to σ̃(n), σ̂(n), and σ̃3(n), respectively, and then we evaluate them in terms of two parameters x and z in Ramanujan’s theory of ell...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Number Theory

سال: 2013

ISSN: 0022-314X

DOI: 10.1016/j.jnt.2013.04.003