Results 1 to 10 of about 52,742 (268)
The spectral decomposition of shifted convolution sums [PDF]
, 2007 We obtain a spectral decomposition of shifted convolution sums in Hecke eigenvalues of holomorphic or Maass cusp forms.Comment: 15 pages, LaTeX2e; v2: corrected and slightly expanded ...
Blomer, Valentin, Harcos, Gergely
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Bernoulli Identities and Combinatoric Convolution Sums with Odd Divisor Functions [PDF]
Abstract and Applied Analysis, 2014 We study the combinatoric convolution sums involving odd divisor functions, their relations to Bernoulli numbers, and some interesting applications.
Daeyeoul Kim, Yoon Kyung Park
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Convolution formula for the sums of generalized Dirichlet L-functions [PDF]
, 2018 Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet $L$-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square $L$-functions and an ...
Balkanova, Olga, Frolenkov, Dmitry
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Evaluation of the convolution sums ∑al+bm=n lσ(l) σ(m) with ab ≤ 9
Open Mathematics, 2017 The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight.
Park Yoon Kyung
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Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8
Open MathematicsIn this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
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Geometric Properties of Meromorphic Functions Involving Convolution Operator
Al-Mustansiriyah Journal of Science, 2022 We introduce and study a subclass of meromorphic univalent functions with positive coefficients defined by a novel operator and obtain coefficient estimates, closure theorems, convolution properties, partial sums, and δ- neighborhood for the class .
Ismael Ibrahim Hameed +1 more
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The multinomial convolution sum of a generalized divisor function
Open Mathematics, 2022 The main theorem of this article is to evaluate and express the multinomial convolution sum of the divisor function σr♯(n;N/4,N){\sigma }_{r}^{\sharp }\left(n;\hspace{0.33em}N\hspace{-0.08em}\text{/}\hspace{-0.08em}4,N) in as a simple form as possible ...
Park Ho
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On the Chebyshev polynomials and some of their new identities
Advances in Difference Equations, 2020 The main purpose of this paper is, using the elementary methods and properties of the power series, to study the computational problem of the convolution sums of Chebyshev polynomials and Fibonacci polynomials and to give some new and interesting ...
Di Han, Xingxing Lv
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Certain Class of Analytic Functions Connected with q-Analogue of the Bessel Function
Journal of Mathematics, 2021 The focus of this article is the introduction of a new subclass of analytic functions involving q-analogue of the Bessel function and obtained coefficient inequities, growth and distortion properties, radii of close-to-convexity, and starlikeness, as ...
Nazek Alessa +5 more
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On predictors for band-limited and high-frequency time series [PDF]
, 2012 Pathwise predictability and predictors for discrete time processes are studied in deterministic setting. It is suggested to approximate convolution sums over future times by convolution sums over past time. It is shown that all band-limited processes are
Dokuchaev +10 more
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