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Article
On a Conjecture of Petrov and Tolev Related to Chen’s Theorem
For any real number y, let [y] be the largest integer not exceeding y. Petrov and Tolev conjectured that there exists a constant \(c_{0}>1\) ...
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Article
Open AccessE-GWAS: an ensemble-like GWAS strategy that provides effective control over false positive rates without decreasing true positives
Genome-wide association studies (GWAS) are an effective way to explore genotype–phenotype associations in humans, animals, and plants. Various GWAS methods have been developed based on different genetic or sta...
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Article
Sum of higher divisor function with prime summands
Let l ≽ 2 be an integer. Recently, Hu and Lü offered the asymptotic formula for the sum of the higher divisor function $$\sum\limits_{1 \leqsl...
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Article
Sums of the higher divisor function of diagonal homogeneous forms
We give an asymptotic formula for \(\sum _{1\le n_1.n_2, \ldots ,n_l\le x^{1/r}}\tau _k(n^r_1+n^r_2+\ldots +n^r_l)\) ...
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Article
On Sums and Products in a Field
We study sums and products in a field. Let F be a field with ch(F) ≠ 2, where ch(F) is the characteristic of F. For any integer k ⩾ 4, we show that any x ∈ F can be written as a1 + … + ak with a1, …, ak ∈ F and a
