Diophantine approximation with prime variables and mixed powers

被引：1

作者：

Li, Boyang ^{[1
]}

Wang, Yuchao ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, 99 Shangda Rd, Shanghai 200444, Peoples R China

来源：

RAMANUJAN JOURNAL | 2023年 / 60卷 / 02期

关键词：

Circle method; Sieve methods; Diophantine inequalities; Prime; SQUARES; SUMS;

D O I：

10.1007/s11139-022-00587-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Assume that lambda(1), center dot center dot center dot, lambda(4) are positive real numbers with lambda(1)/lambda(2) irrational and algebraic. Let V be a well-spaced sequence and delta > 0. For any given positive integer k >= 4 and any epsilon > 0, we improve the upper bound of the number of v is an element of V with v <= X for which the inequality vertical bar lambda(1)p(2)(2 ) + lambda(2)p(2)(2) + lambda(3)p(3)(3) + lambda P-4(4)k - v vertical bar < v(-delta )has no solution in primes p(1), center dot center dot center dot, P-4.

引用

页码：371 / 389

页数：19

共 15 条

[1] Proof of the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three [J].

Bourgain, Jean ;

Demeter, Ciprian ;

Guth, Larry .

ANNALS OF MATHEMATICS, 2016, 184 (02) :633-682

[2]

Davenport H., 1946, J. London Math. Soc., V21, P185

[3]

Feng Z.Z., 2019, The exceptional sets for Waring-Goldbach problem

[4] The values of ternary quadratic forms at prime arguments [J].

Harman, G .

MATHEMATIKA, 2004, 51 (101-02) :83-96

[5] On sums of squares of primes [J].

Harman, G ;

Kumchev, AV .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2006, 140 :1-13

[6]

[李伟平 Li Weiping], 2010, [数学年刊. A辑, Chinese Annals of Mathematics, Ser. A], V31, P247

[7] A note on Diophantine approximation with prime variables and mixed powers [J].

Liu, Huafeng .

RAMANUJAN JOURNAL, 2021, 56 (01) :249-263

[8] Diophantine Approximation with Mixed Powers of Primes [J].

Liu, Huafeng ;

Huang, Jing .

TAIWANESE JOURNAL OF MATHEMATICS, 2019, 23 (05) :1073-1090

[9] Diophantine approximation with mixed powers of primes [J].

Liu, Yuhui .

RAMANUJAN JOURNAL, 2021, 56 (02) :411-423

[10] On sums of squares of primes and a k-th power of prime [J].

Liu, Zhixin ;

Zhang, Rui .

MONATSHEFTE FUR MATHEMATIK, 2019, 188 (02) :269-285

← 1 2 →