Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface d...Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u^(3)=Q(y)z.We can get a power-saving result for a class of special quadratic forms and improve on some previous work.展开更多
Let c>1 and 0<γ<1.We study the solubility of the Diophantine inequality∣p^(c)_(1)+p^(c)_(2)+…+p^(c)_(s)−N∣<(log N)^(−1) in Piatetski-Shapiro primes p_(1),p_(2),…,p_(s) of the form pj=[m^(1/γ)]for som...Let c>1 and 0<γ<1.We study the solubility of the Diophantine inequality∣p^(c)_(1)+p^(c)_(2)+…+p^(c)_(s)−N∣<(log N)^(−1) in Piatetski-Shapiro primes p_(1),p_(2),…,p_(s) of the form pj=[m^(1/γ)]for some m∈ℕ,and improve the previous results in the cases s=2,3,4.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11971476).
文摘Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u^(3)=Q(y)z.We can get a power-saving result for a class of special quadratic forms and improve on some previous work.
基金the National Natural Science Foundation of China(Grant No.11701596)the Science and Technology Development Fund,Macao SAR(File No.049/2017/A)the National Natural Science Foundation of China(Grant.No.11971476).
文摘We study the mean square of the error term of the mean value for binary Egyptian fractions.We get an asymptotic formula under the Riemann Hypothesis.
基金The authors would like to express their gratitude to the referee for his or her careful reading and valuable suggestionsThis work was supported by the National Natural Science Foundation of China(Grant Nos.11771256,11971476).
文摘Let c>1 and 0<γ<1.We study the solubility of the Diophantine inequality∣p^(c)_(1)+p^(c)_(2)+…+p^(c)_(s)−N∣<(log N)^(−1) in Piatetski-Shapiro primes p_(1),p_(2),…,p_(s) of the form pj=[m^(1/γ)]for some m∈ℕ,and improve the previous results in the cases s=2,3,4.
