Results 21 to 30 of about 2,222 (176)
The fractional sum of small arithmetic functions [PDF]
Journal of Number Theory, 2021 where f is an arithmetic function and ⌊·⌋ denotes the greatest integer function. When f(n) = n, this is the classic Dirichlet divisor problem. Such sums do not seem to have a name in the literature yet, so we propose to call Sf the “fractional sum of f .”
Joshua Stucky
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On Certain Sums of Arithmetic Functions Involving the GCD and LCM of Two Positive Integers [PDF]
Results in Mathematics, 2020 We obtain asymptotic formulas with remainder terms for the hyperbolic summations ∑mn≤xf((m,n))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
Randell Heyman, L. T'oth
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On some new results for the generalised Lucas sequences [PDF]
, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica, D., Turcaş, G.C., Bagdasar, O.
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GOLDBACH REPRESENTATIONS IN ARITHMETIC PROGRESSIONS AND ZEROS OF DIRICHLET L ‐FUNCTIONS [PDF]
Mathematika, 2017 Assuming a conjecture on distinct zeros of Dirichlet L-functions we get asymptotic results on the average number of representations of an integer as the sum of two primes in arithmetic progression.
G. Bhowmik +3 more
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On some results of Indlekofer for multiplicative functions II.
Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, 2023 In this paper we describe how convolution arithmetic is be used for the investigation of the asymptotic mean behaviour of multiplicative functions.
Erdener Kaya
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Filomat, 2023 Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group ? = SL(2,Z), and let ?f (n), ?(n) and ?(n) be the nth normalized Fourier coefficient of the cusp form f , the sum-of-divisors function and the ...
Guodong Hua
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On some problems involving Dirichlet L-functions [PDF]
, 2023 In this thesis we study three problems in analytic number theory. These problems are related at a fundamental level, but a general introduction to those relationships would digress from the subsequent content and a summary would certainly be superficial.
K Smith (7711202)
core
Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization [PDF]
Mathematics, 2011 We consider a wide class of summatory functions Ff;N,pm=∑k≤Nfpmk, m∈Z+∪{0} associated with the multiplicative arithmetic functions f of a scaled variable k∈Z+, where p is a prime number. Assuming an asymptotic behavior of the summatory function, F{f;N,1}=
L. Fel
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Properties of the series solution for Painlevé I [PDF]
, 2013 We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painlevé equation.
Ragnisco, Orlando +3 more
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Elliptic Combinatorics and Markov Processes [PDF]
, 2012 We present combinatorial and probabilistic interpretations of recent results in the theory of elliptic special functions (due to, among many others, Frenkel, Turaev, Spiridonov, and Zhedanov in the case of univariate functions, and Rains in the ...
Betea, Dan Dumitru
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