Publications related to Direct sum

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A new elementary proof of the Prime Number Theorem

Florian Karl Richter

Let

\Omega(n)

denote the number of prime factors of

n

. We show that for any bounded

f\colon\mathbb{N}\to\mathbb{C}

one has [ \frac{1}{N}\sum_{n=1}^N, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). ] This yields a ...

2021

Direct sum

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Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization

Stochastic distributed learning with gradient quantization and double-variance reduction

Idempotents in the endomorphism algebra of a finite lattice

Intermolecular Pd(0)-Catalyzed Atropo-enantioselective C-H Arylation of Heteroarenes and Other Investigations into the Enantioselective Activation of Challenging C(sp3)-H Bonds

A generalized theory of separable effects in competing event settings

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

The effects of Prandtl number on the nonlinear dynamics of Kelvin-Helmholtz instability in two dimensions

A new elementary proof of the Prime Number Theorem

Development of remote C-H bond functionalization of redox-active alcohol derivatives and oxidative transformations under photoredox catalysis

Poly-NL: Linear Complexity Non-local Layers With 3rd Order Polynomials

Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization

Stochastic distributed learning with gradient quantization and double-variance reduction

Idempotents in the endomorphism algebra of a finite lattice

A generalized theory of separable effects in competing event settings

The effects of Prandtl number on the nonlinear dynamics of Kelvin-Helmholtz instability in two dimensions

A new elementary proof of the Prime Number Theorem

Poly-NL: Linear Complexity Non-local Layers With 3rd Order Polynomials

Development of remote C-H bond functionalization of redox-active alcohol derivatives and oxidative transformations under photoredox catalysis

Intermolecular Pd(0)-Catalyzed Atropo-enantioselective C-H Arylation of Heteroarenes and Other Investigations into the Enantioselective Activation of Challenging C(sp3)-H Bonds

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes