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Trigonometric analogues of the identities associated with twisted sums of divisor functions

The Ramanujan Journal
Inspired by two entries published in Ramanujan's lost notebook on Page 355, B. C. Berndt et al.\cite{MR3351542} presented Riesz sum identities for Ramanujan entries by introducing the twisted divisor sums. Later, S. Kim \cite{MR3541702} derived analogous results by replacing twisted divisor sums with twisted sums of divisor functions.
Banerjee, Debika, Khurana, Khyati
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Sum of Divisors Function And The Largest Integer Function Over The Shifted Primes

, 2021
Let $ x\geq 1 $ be a large number, let $ [x]=x-\{x\} $ be the largest integer function, and let $ (n)$ be the sum of divisors function. This note presents the first proof of the asymptotic formula for the average order $ \sum_{p\leq x} ([x/p])=c_0x\log \log x+O(x) $ over the primes, where $c_0>0$ is a constant. More generally, $ \sum_{p\leq x} ([
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A note on generating identities for multiplicative arithmetic functions [PDF]

Contributions to Mathematics
Karol Gryszka
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Mean Value Estimation of The Sum-of-divisors Function

Journal of Innovation and Development
 The sum-of-divisor function is one of the important number theory functions, and the study of the properties of the sum-of-divisor function can provide more methods for solving some number theory problems. Since the value of the function is irregular with the change of the independent variables, the mean estimation of the sum-of-divisor function is ...
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A Note on Large Sums of Divisor-Bounded Multiplicative Functions

16 pages, project begun at Women in Numbers ...
Frechette, Claire, Gerbelli-Gauthier, Mathilde, Hamieh, Alia, Tanabe, Naomi   +3 more
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Solutions to some sign change problems on functions involving sums of divisors

Periodica Mathematica Hungarica
In this note, we solve some sign change problems on the functions involving sums of divisors posed by Pongsriiam recently.
Ding, Yuchen, Pan, Hao, Sun, Yu-Chen
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Multiplicative structures of values of the sum-of-divisors function

, 2005
We study equations of the form $ (p^{q-1})=Az$, where $p$ is a prime, $q$ is a fixed odd prime, $A$ is a fixed integer and $z$ is an integer composed of primes in a fixed finite set. We shall improve upper bounds for the size and the number of solutions of such equations.
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On the variance of sums of divisor functions in short intervals

Proceedings of the American Mathematical Society, 2016
Given a positive integer $n$ the $k$-fold divisor function $d_k(n)$ equals the number of ordered $k$-tuples of positive integers whose product equals $n$. In this article we study the variance of sums of $d_k(n)$ in short intervals and establish asymptotic formulas for the variance of sums of $d_k(n)$ in short intervals of certain lengths for $k=3$ and
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Matroid psi classes. [PDF]

Sel Math New Ser, 2022
Dastidar J, Ross D.
europepmc   +1 more source

Extreme values of derivatives of the Riemann zeta function. [PDF]

Mathematika, 2022
Yang D.
europepmc   +1 more source