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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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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 $\mid\Sigma_{2n}\mid\sim 2n^2/\log^2{n}$ as $n\to\infty$. We also assume that a partition is selected uniformly at
Mutafchiev, Ljuben
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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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On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 The Goldbach partitions of an even number, given by the sums of two prime addends, form the nonempty set for all integers 2n with 2≤n≤2×1014. It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the
Simon Davis
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, 2020 We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can perform on a ...
Dailly, Antoine +3 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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EXPLORING SOME NEW IDEAS ON SMARANDACHE TYPE SETS, FUNCTIONS AND SEQUENCES [PDF]
, 1996 In this article I have defined a number of SMARANDACHE type sets ,sequences which I found very interesting. The problems and conjectures proposed would give food for thought and would pave ways for more work in this ...
Murthy, A.
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Empirical Significance, Predictive Power, and Explication [PDF]
, 2017 Criteria of empirical significance are supposed to state conditions under which (putative) reference to an unobservable object or property is “empirically meaningful.” The intended kind of empirical meaningfulness should be necessary for admissibility ...
Surovell, Jonathan/R
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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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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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