Evaluation of the convolution sums ∑++=σ(k)σ(l)σ(m) with lcm(a,b,c)≤6
نویسندگان
چکیده
منابع مشابه
the evaluation of language related engagment and task related engagment with the purpose of investigating the effect of metatalk and task typology
abstract while task-based instruction is considered as the most effective way to learn a language in the related literature, it is oversimplified on various grounds. different variables may affect how students are engaged with not only the language but also with the task itself. the present study was conducted to investigate language and task related engagement on the basis of the task typolog...
15 صفحه اولThe 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
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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 کاملShifted 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).
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2016.04.025