Results 1 to 10 of about 138 (120)
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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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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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.
Ljuben Mutafchiev
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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.
Ricardo Jesus +2 more
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On the Distribution of the Number of Goldbach Partitions of a Randomly Chosen Positive Even Integer [PDF]
Electronic Notes in Discrete Mathematics, 2016 Let $\mathcal{P}=\{p_1,p_2,...\}$ be the set of all odd primes arranged in increasing order. A Goldbach partition of the even integer $2k>4$ is a way of writing it as a sum of two primes from $\mathcal{P}$ without regard to order. Let $Q(2k)$ be the number of all Goldbach partitions of the number $2k$.
Ljuben Mutafchiev
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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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Efficient Approximation of Goldbach Partition Function Using Machine Learning Models
IEEE AccessGoldbach’s conjecture, still unproven, posits that every even integer greater than 2 can be expressed as the sum of two primes. The Goldbach partition function $G(n)$ counts the number of such prime pairs for even integer $n \gt 2$ .
Cheng-Zhe Wu, Shyong Jian Shyu
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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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On Partitions of Goldbach's Conjecture
, 2000 An approximate formula for the partitions of Goldbach's Conjecture is derived using Prime Number Theorem and a heuristic probabilistic approach. A strong form of Goldbach's conjecture follows in the form of a lower bounding function for the partitions of Goldbach's conjecture.
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