Results 1 to 10 of about 1,032 (103)
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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Prime numbers, quantum field theory and the Goldbach conjecture [PDF]
, 2012 Motivated by the Goldbach conjecture in Number Theory and the abelian bosonization mechanism on a cylindrical two-dimensional spacetime we study the reconstruction of a real scalar field as a product of two real fermion (so-called \textit{prime}) fields ...
Di Francesco P. +6 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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A q-analog of Euler's decomposition formula for the double zeta function [PDF]
, 2005 The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler's results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum
Bradley, David M.
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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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Pauli graphs, Riemann hypothesis, Goldbach pairs [PDF]
, 2011 Let consider the Pauli group $\mathcal{P}_q=$ with unitary quantum generators $X$ (shift) and $Z$ (clock) acting on the vectors of the $q$-dimensional Hilbert space via $X|s> =|s+1>$ and $Z|s> =\omega^s |s>$, with $\omega=\exp(2i\pi/q)$.
A. Vourdas +17 more
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The conjecturing process: perspectives in theory and implications in practice [PDF]
, 2007 In this paper we analyze different types and stages of the conjecturing process. A classification of conjectures is discussed. A variety of problems that could lead to conjectures are considered from the didactical point of view. Results from a number of
Cañadas, María C. +4 more
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Finite connected components of the aliquot graph [PDF]
, 2017 Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than $10^9$, as well as those containing an amicable pair below $10^{14}$ or one of the known perfect or ...
Booker, Andrew R.
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