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  • 期刊=Frontiers of Mathematics in Chinax
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Inverse problems associated with subsequence sums in Cp■Cp
《Frontiers of Mathematics in China》2020年第5期985-1000,共16页Jiangtao PENG Yongke QU Yuanlin LI 
supported in part by the Fundamental Research Funds for the Central Universities(No.3122019152);the National Natural Science Foundation of China(Grant Nos.11701256,11871258);the Youth Backbone Teacher Foundation of Henan's University(No.2019GGJS196);the China Scholarship Council(Grant No.201908410132);was also supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN 2017-03903).
Let G be a finite abelian group and S be a sequence with elements of G.We say that S is a regular sequence over G if|SH|≤|H|-1 holds for every proper subgroup H of G,where SH denotes the subsequence of S consisting o...
关键词：Inverse problems subsequence sums regular sequences zZero-sumfree sequences 
Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes
《Frontiers of Mathematics in China》2019年第5期1017-1035,共19页Rui ZHANG 
The author would like to express the most sincere gratitude to Prof.Zhixin Liu for his valuable advice and constant encouragement;This work was supported by the National Natural Science Foundation of China(Grant No.11871367).
We prove that,with at most O(N17/192+ε)exceptions,all even positive integers up to N are expressible in the form P1^2+P2^2+P3^3+P5^4+P6^4,where Pi,P2,……,P6 are prime numbers.This gives large improvement of a recent...
关键词：Waring-Goldbach problem circle method exceptional set 
Averages of shifted convolution sums for arithmetic functions
《Frontiers of Mathematics in China》2019年第1期123-134,共12页Miao LOU 
Let f be a full-level cusp form for GLm(Z) with Fourier coefficients Af(cm-2,…, c1, n): Let λ(n) be either the von Mangoldt function Λ(n) or the k-th divisor function τk(n): We consider averages of shifted convolu...
关键词：AVERAGE shifted CONVOLUTION SUM ARITHMETIC function 
Sums of Fourier coefficients of cusp forms of level D twisted by exponential functions
《Frontiers of Mathematics in China》2017年第3期655-673,共19页Huan LIU 
This work was supported in part by the Natural Science Foundation of Shandong Province （No. ZR2015AM016）.
Let g be a holomorphic or Maass Hecke newform of level D and nebentypus XD, and let ag（n） be its n-th Fourier coefficient. We consider the sum S1=∑ X〈n≤2x ag（n）e（an β） and prove that S1 has an asymptotic for...
关键词：exponential sums cusp form Fourier coefficients 
Precise large deviations for sums of random vectors with dependent components of consistently varying tails被引量：1
《Frontiers of Mathematics in China》2017年第3期711-732,共22页Xinmei SHEN Yuqing NIU Hailan TIAN 
Let {Xi = （X1,i,...,Xm,i）T, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying...
关键词：Precise large deviations MULTI-DIMENSIONAL consistently varying distributions random sums 
Sums of nine almost equal prime cubes被引量：1
《Frontiers of Mathematics in China》2014年第5期1131-1140,共10页Yanjun YAO 
We prove that each sufficiently large odd integer N can be written as sum of the form N = p1^3 ＋p2^3 ＋... ＋p9^3 with [pj - （N/9）^1/31 ≤ N^（1/3）-θ, where pj, j = 1,2,...,9, are primes and θ = （1/51） -ε.
关键词：Waring-Goldbach problem circle method exponential sum overprimes in short intervals 
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