Results 1 to 10 of about 7,457,680 (317)
Dimension of the exceptional set in the Aronszajn-Donoghue theorem for finite rank perturbations [PDF]
International mathematics research notices, 2020 The classical Aronszajn-Donoghue theorem states that for a rank one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular.
Liaw, Constanze +2 more
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Exceptional Set Estimate Through Brascamp–Lieb Inequality [PDF]
International Mathematics Research Notices, 2023 Fix integers $1\le ...
Shengwen Gan
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Exceptional sets for Diophantine inequalities [PDF]
International Mathematics Research Notices, 2012 We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument.
D. Wooley, Scott T. Parsell, Trevor
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Exceptional set of Goldbach number
Journal of Number Theory, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
W. Lu
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The exceptional set of Goldbach numbers (II) [PDF]
Acta Arithmetica, 2000 Numbers which are sums of two odd primes are called Goldbach numbers. Let \(E(x)\) denote the number of even numbers up to \(x\) which are not Goldbach numbers, so that the Goldbach conjecture is that \(E(x)=2\) for every \(x\geq 4\). \textit{H. L. Montgomery} and \textit{R. C. Vaughan} [Acta Arith. 27, 353-370 (1975; Zbl 0301.10043)] first proved that
Hongze Li
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A Zariski dense exceptional set in Manin’s Conjecture: dimension 2 [PDF]
Research in Number Theory, 2022 Recently, Lehmann, Sengupta, and Tanimoto proposed a conjectural construction of the exceptional set in Manin’s Conjecture, which we call the geometric exceptional set.
Runxuan Gao
semanticscholar +1 more source
Contemporary Mathematics. Fundamental Directions, 2023 In this paper, we study sequences of complex numbers of the first order. Multiple terms are allowed for such sequences. We also consider complex sequences with a finite maximum density. We construct special coverings of multiple sets {λk,nk} consisting of circles centered at points λk of special radii.
Krivosheev, A. S., Krivosheeva, O. A.
openaire +2 more sources
The exceptional sets of a Waring-Goldbach problem with unequal powers
Xi'an Gongcheng Daxue xuebao, 2021 The representability of positive odd number n=p1+P32+p3k(k∈N and k≥4) was studied. The circle method in additive number theory and the iterative method in the circle method were used to deal with the main arcs and the exponential sum method was used to ...
Doudou ZHU
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Exceptional set in Waring–Goldbach problem for sums of one square and five cubes
AIMS Mathematics, 2022 Let $ N $ be a sufficiently large integer. In this paper, it is proved that, with at most $ O\big(N^{4/9+\varepsilon}\big) $ exceptions, all even positive integers up to $ N $ can be represented in the form $ p_1^2+p_2^3+p_3^3+p_4^3+p_5^3+p_6^3 $, where $
Jinjiang Li +3 more
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On the Waring-Goldbach problem for two squares and four cubes
Open Mathematics, 2023 Let NN be a sufficiently large integer. In this article, it is proved that, with at most O(N112+ε)O\left({N}^{\tfrac{1}{12}+\varepsilon }) exceptions, all even positive integers up to NN can be represented in the form p12+p22+p33+p43+p53+p63{p}_{1}^{2 ...
Zhang Min, Bai Hongxin, Li Jinjiang
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