Results 1 to 10 of about 113 (107)
Goldbach partitions and norms of cusp forms
Journal of Numerical Analysis and Approximation Theory, 2019 An integral formula for the Goldbach partitions requires uniform convergence of a complex exponential sum. The dependence of the coefficients of the series is found to be bounded by that of cusp forms.
Simon Brian Davis
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Vectorizing and distributing number‐theoretic transform to count Goldbach partitions on Arm‐based supercomputers [PDF]
Concurrency and Computation: Practice and Experience, 2023 SummaryIn this article, we explore the usage of scalable vector extension (SVE) to vectorize number‐theoretic transforms (NTTs). In particular, we show that 64‐bit modular arithmetic operations, including modular multiplication, can be efficiently implemented with SVE instructions.
Jesus, Ricardo +2 more
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Complex Circles of Partition and the Asymptotic Binary Goldbach Conjecture
, 2022 In this work, we continue the complex circle of partition development that was started in our foundational study [3]. With regard to commandits embedding circle, we define interior and exterior points. On this foundation, we expand the concept of point density, established in [2], to include complex circles of partition.
Theophilus Agama, Berndt Gensel
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Philosophical Perspectives, Volume 37, Issue 1, Page 145-163, December 2023., 2023 Abstract Some conditional involving factive emotives present a prima facie challenge to the thesis that conditionals obey modus ponens. Drawing on recent work by Timothy Williamson, I offer an error‐theoretic diagnosis of the phenomenon, one that appeals to a heuristic that we use in suppositional reasoning.
Christina Hope Dietz
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Physiologia Plantarum, Volume 175, Issue 6, November/December 2023., 2023 Abstract Soil phosphorus (P) application is the most common fertilisation technique but may involve constraints due to chemical fixation and microbial immobilisation. Furthermore, excessive P fertilisation leads to P runoff into water bodies, threatening ecosystems, so targeted foliar P fertilisation is an interesting alternative.
Jon Niklas Henningsen +5 more
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A Note on Goldbach Partitions of Large Even Integers [PDF]
The Electronic Journal of Combinatorics, 2015 Let $\Sigma_{2n}$ be the set of all partitions of the even integers from the interval $(4,2n], n>2,$ into two odd prime parts. We show that $|\Sigma_{2n}| \sim 2n^2/\log^2{n}$ as $n\to\infty$. We also assume that a partition is selected uniformly at random from the set $\Sigma_{2n}$. Let $2X_n\in (4,2n]$ be the size of this partition.
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Fractal in the statistics of Goldbach partition
, 2006 Some interesting chaos phenomena have been found in the difference of prime numbers. Here we discuss a theme about the sum of two prime numbers, Goldbach conjecture. This conjecture states that any even number could be expressed as the sum of two prime numbers.
Liang, Wang, Yan, Huang, Zhi-cheng, Dai
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SciPost Physics CoreThe famous Goldbach conjecture states that any even natural number $N$ greater than $2$ can be written as the sum of two prime numbers $p^{\text{(I)}}$ and $p^{\text{(II)}}$.
Oleksandr V. Marchukov, Andrea Trombettoni, Giuseppe Mussardo, Maxim Olshanii
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Divisor Goldbach Conjecture and its Partition Number
, 2016 Based on the Goldbach conjecture and arithmetic fundamental theorem, the Goldbach conjecture was extended to more general situations, i.e., any positive integer can be written as summation of some specific prime numbers, which depends on the divisible factor of this integer, that is: For any positive integer $n~(n>2)$, if there exists an integer $m$,
Kun, Yan, Biao, Li Hou
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Effects of temporal and spatial variability in energy fluxes on phytoplankton
Limnology and Oceanography, Volume 71, Issue 1, January 2026.Abstract Climate change has significantly altered the energy dynamics of lakes; however, little is known of how the temporal and spatial variation in energy fluxes impacts the structure and function of lake ecosystems. This study combined long‐term (2011–2018) measurements of lake energy fluxes with environmental, nutrient, and phytoplankton data at ...
Jian Zhou +4 more
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