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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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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
exaly +3 more sources
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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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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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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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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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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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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