Zobrazeno 1 - 10
of 5 103
pro vyhledávání: '"$ l $-function"'
Publikováno v:
AIMS Mathematics, Vol 9, Iss 9, Pp 25166-25183 (2024)
Let $ \lambda_f(n) $ be the $ n $th normalized Fourier coefficient of a holomorphic cusp form $ f $ for the full modular group. In this paper, we established asymptotic formulae for high power sums of Fourier coefficients of cusp forms and further im
Externí odkaz:
https://doaj.org/article/06080a70710f40d4ab21538dd1569784
Autor:
Xianghu Liu, Yanfang Li
Publikováno v:
Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-14 (2024)
Abstract This study is centered on the optimal controllability of differential equations involving fractional derivatives of Katugampola. We derive both necessary and sufficient conditions for optimal controllability by extending Gronwall’s inequal
Externí odkaz:
https://doaj.org/article/74b0617ecfd441c1bd16410f60a15516
Autor:
Zhenjiang Pan, Zhengang Wu
Publikováno v:
AIMS Mathematics, Vol 9, Iss 6, Pp 16564-16585 (2024)
In this paper, we derive the asymptotic formulas $ B^*_{r, s, t}(n) $ such that $ \mathop{\lim} \limits_{n \rightarrow \infty} \left\{ \left( \sum\limits^{\infty}_{k = n} \frac{1}{k^r(k+t)^s} \right)^{-1} - B^*_{r,s,t}(n) \right\} = 0, $ where
Externí odkaz:
https://doaj.org/article/0c9acae53be64923a6ebcbe946741a8e
Autor:
Zhuoyu Chen, Wenpeng Zhang
Publikováno v:
AIMS Mathematics, Vol 9, Iss 5, Pp 12814-12824 (2024)
Our main purpose of this article was using the analytic methods and the properties of Dirichlet $ L $-functions to study the properties of Dedekind sums and give a new reciprocity formula for it. As its applications, some exact calculating formula fo
Externí odkaz:
https://doaj.org/article/591d94722dd34fa4b86fe192696f7014
Autor:
Bin Guan
Publikováno v:
AIMS Mathematics, Vol 9, Iss 2, Pp 4896-4906 (2024)
In this paper, we prove a prime number theorem in short intervals for the Rankin-Selberg $ L $-function $ L(s, \phi\times\phi) $, where $ \phi $ is a fixed dihedral Maass newform. As an application, we give a lower bound for the proportion of primes
Externí odkaz:
https://doaj.org/article/523679df4ae44e5288ead59d93ae368b
Autor:
Huafeng Liu, Rui Liu
Publikováno v:
AIMS Mathematics, Vol 9, Iss 2, Pp 4830-4843 (2024)
Let $ \lambda_{f}(n) $ be the $ n $-th normalized Fourier coefficient of $ f $, which is a primitive holomorphic cusp form of even integral weight $ k\geq2 $ for the full modular group $ SL_2(\mathbb{Z}) $. Let also $ \sigma(n) $ and $ \phi(n) $ be t
Externí odkaz:
https://doaj.org/article/d72f41b7e7e14396ac549191f65b0d2a
Autor:
Abhijit Banerjee, Arpita Kundu
Publikováno v:
Cubo, Vol 25, Iss 3, Pp 497-514 (2023)
In this article, we have mainly focused on the uniqueness problem of an \(L\)-function \(\mathcal{L}\) with an \(L\)-function or a meromorphic function \(f\) under the condition of sharing the sets, generated from the zero set of some strong uniquene
Externí odkaz:
https://doaj.org/article/f805b79ef9124a9fbb529efa5144943c