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The arithmetic derivative and Leibniz-additive functions [PDF]
Annales Mathematicae et Informaticae, 2018 An arithmetic function $f$ is Leibniz-additive if there is a completely multiplicative function $h_f$, i.e., $h_f(1)=1$ and $h_f(mn)=h_f(m)h_f(n)$ for all positive integers $m$ and $n$, satisfying $$ f(mn)=f(m)h_f(n)+f(n)h_f(m) $$ for all positive ...
Haukkanen, Pentti +2 more
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On an additive arithmetic function [PDF]
, 1977 We discuss in this paper arithmetic properties of the function A(n) = Σ p a Un ap. Asymptotic estimates of A(n) reveal the connection between A(n) and large prime factors of n.
Krishnaswami Alladi, P. Erdős
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Differentiability of the arithmetic volume function [PDF]
Journal of the London Mathematical Society, 2008 We introduce the positive intersection product in Arakelov geometry and prove that the arithmetic volume function is continuously differentiable. As applications, we compute the distribution function of the asymptotic measure of a Hermitian line bundle ...
Chen, Huayi
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The Riemann-zeta function on vertical arithmetic progressions [PDF]
, 2012 We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression $1/2 + i(an + b)$ with $a > 0$, $b$ real, exhibits a remarkable correspondance with the analogous continuous average and derive several ...
Li, Xiannan, Radziwill, Maksym
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Frontal Midline Theta Oscillations during Mental Arithmetic: Effects of Stress
Frontiers in Behavioral Neuroscience, 2015 Complex cognitive tasks such as mental arithmetic heavily rely on intact, well-coordinated prefrontal cortex (PFC) function. Converging evidence suggests that frontal midline theta (FMT) oscillations play an important role during the execution of such ...
Matti eGärtner +5 more
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Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models [PDF]
Neural Information Processing Systems, 2023 Task arithmetic has recently emerged as a cost-effective and scalable approach to edit pre-trained models directly in weight space: By adding the fine-tuned weights of different tasks, the model's performance can be improved on these tasks, while ...
Guillermo Ortiz-Jiménez +2 more
semanticscholar +1 more source
A simple proof of generalizations of number-theoretic sums [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 For positive integers 𝑘, 𝑚, and 𝑛, let 𝑆𝑘 𝑚(𝑛) be the sum of all elements in the finite set {𝑥 𝑘 : 1 ≤ 𝑥 ≤ 𝑛⁄𝑚 , (𝑥, 𝑛) = 1}. The formula for 𝑆𝑘 𝑚(𝑛) is established and simpler formulae for 𝑆𝑘 𝑚(𝑛) under some conditions on 𝑚 and 𝑛 are verified. The
Yanapat Tongron +1 more
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Teaching Arithmetic to Small Transformers [PDF]
arXiv.org, 2023 Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction ...
Nayoung Lee +4 more
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Density of Arithmetic Representations of Function Fields [PDF]
Épijournal de Géométrie Algébrique, 2022 We propose a conjecture on the density of arithmetic points in the deformation space of representations of the \'etale fundamental group in positive characteristic. This?
Hélène Esnault, Moritz Kerz
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