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Paper R5 v2.2 — Spectral-Budget Isomorphism: The von Mangoldt Function from XOR-Annihilation and Closure Depth

Paper R5 v2.2 — Spectral-Budget Isomorphism:The von Mangoldt Function from XOR-Annihilation and Closure Depth Authors: Fedor KapitanovPublication Date: June 2026Status: Closed — Derived v2.2 Overview We close open problem OP-R5 of the ORT Riemann programme by proving the Spectral-Budget Isomorphism: Tr(Bnbm) = C · Λ(m ...
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Paper R5 v1.1 Spectral-Budget Isomorphism: The von Mangoldt Function from XOR-Annihilation and Closure Depth

Paper R5 v1.1 — Spectral-Budget Isomorphism:The von Mangoldt Function from XOR-Annihilation and Closure Depth Authors: Fedor KapitanovPublication Date: June 2026Status: Closed — Derived Overview We close open problem OP-R5 of the ORT Riemann programme by proving the Spectral-Budget Isomorphism: Tr(Bnbm) = C · Λ(m) where &
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Paper R5 v 3.0 Spectral-Budget Isomorphism: The von Mangoldt Function from XOR-Annihilation and Closure Depth

Paper R5 v3.0   Author: Fedor KapitanovDate: June 2026Status: Closing OP-R5 of the ORT Riemann programme Result We close open problem OP-R5 by proving the Spectral-Budget Isomorphism: Tr(Bnbm) = C · Λ(m) where Λ(m) is the von Mangoldt function and C is a carrier normalisation constant. Method The derivation uses no external
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On certain sums involving von Mangoldt's function in short intervals

, 1980
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On Sums of Sums Involving the Von Mangoldt Function

Results in Mathematics
In the paper under review, the authors estimate the following sum over the von Mangoldt function, for the values \(k=1,2\) and large real numbers \(x\) and \(y\), \[ S_{k}(x,y):=\sum _{n\le y}\left( \sum _{q\le x}\sum _{d|\gcd(n,q)}d\Lambda \left( \frac{q}{d}\right) \right) ^{k}.
Wataru Takeda, Isao Kiuchi
exaly   +3 more sources

On the von Mangoldt-type function of the Fibonacci zeta function

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas
[EN]The Dirichlet series associated to the Fibonacci sequence $\{F_{n}\}$, $$\sum_{n=1}^{\infty} F_{n}^{-s},$$ converges for $s\in \mathbb{C}$ with $\Re s > 0$. The analytic function $\varphi(s)$ it defines on the right half-plane is known as the Fibonacci zeta function.
Juan Luis Varona, Luis M Navas, Gaspar Mora   +2 more
exaly   +3 more sources

Asymptotic behaviors of some arithmetic function associated with the von Mangoldt function

Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, 2023
Some function associated with the von Mangoldt function is investigated. It is related to the logarithm of the Riemann zeta function. By means of probability theory, we show that this function is bounded above and below by a certain function. It is possible that the result extends to Dirichlet series.
exaly   +2 more sources

Exponential sums formed with the von Mangoldt function and Fourier coefficients of $${ GL}(m)$$ G L ( m ) automorphic forms

Monatshefte Fur Mathematik, 2017
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Yujiao Jiang, Guangshi Lu, Jiang Yujiao   +2 more
exaly   +2 more sources

On fractional sum of the von Mangoldt function

Colloquium Mathematicum
The paper under review belongs to a long line of articles dealing with sums of the shape \[ S_f (x) := \sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right), \] where \(\lfloor t \rfloor\) is the integer part of \(t\) and \(f\) is any usual arithmetic function.
Lü, Xiaodong, Xu, Xinyue
exaly   +2 more sources