지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
오류제보하기
Let $k$ be an integer with $k\geq 3$. Define $h(k)=\left[{\frac{k+1}{2}}\right]$, $\sigma(k)=\min\left(2^{h(k)-1},\,{\frac{1}{2}}h(k)(h(k)+1)\right)$. Suppose that $\lambda_1,\ldots,\lambda_5$ are non-zero real numbers, not all of the same sign, satisfying that $\frac{\lambda_1}{\lambda_2}$ is irrational. Then for any given real number $\eta$ and $\varepsilon>0$, the inequality \begin{align*} |\lambda_1p^2_1+\lambda_2p_2^2+\lambda_3p_3^2+\lambda_4p_4^2+\lambda_5p_5^k+\eta|<(\max_{1\leq j\leq 5} p_j)^{-\frac{3}{20\sigma(k)}+\varepsilon } \end{align*} has infinitely many solutions in prime variables $p_1,\ldots,p_5$. This gives an improvement of the recent results.
목차
등록된 정보가 없습니다.
참고문헌 (12)
참고문헌 신청
J. Brudern / 1997 / The Davenport-Heilbronn Fourier transform method, and some Diophantine inequalities / Number theory and its applications :59~87
W. Ge / 2018 / On Diophantine problems with mixed powers of primes / Acta Arith 182(2):183~199
G. Harman / 2004 / The values of ternary quadratic forms at prime arguments / Mathematika 51(1-2):83~96
G. Harman / 2010 / On sums of squares of primes II / J. Number Theory 130(9):1969~2002
L.-K. Hua / 1938 / Some results in the additive prime-number theory / Quart. J. Math. Oxford Ser 9(1):68~80
W. Ge / 2018 / On Diophantine problems with mixed powers of primes / Acta Arith 182(2):183~199
G. Harman / 2004 / The values of ternary quadratic forms at prime arguments / Mathematika 51(1-2):83~96
G. Harman / 2010 / On sums of squares of primes II / J. Number Theory 130(9):1969~2002
L.-K. Hua / 1938 / Some results in the additive prime-number theory / Quart. J. Math. Oxford Ser 9(1):68~80
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Some conditions on the form of third element from Diophantine pairs and its application
대한수학회지
2018 .01
-
A logarithmic inequality involving prime numbers
Proceedings of the Jangjeon Mathematical Society
2021 .07
-
Integer points on the elliptic curves induced by Diophantine triples
대한수학회논문집
2020 .01
-
On the Diophantine equation $a \left(\frac{b^k - 1}{b - 1}\right) = U_n – U_m$
ANNALS OF FUZZY MATHEMATICS AND INFORMATICS
2024 .06
-
Diophantine triple with Fibonacci numbers and elliptic curve
대한수학회논문집
2021 .01
-
ON THE DIOPHANTINE EQUATION (5pn<sup>2</sup> - 1)<sup>x</sup> + (p(p - 5)n<sup>2</sup> + 1)<sup>y</sup> = (pn)<sup>z</sup>
호남수학학술지
2020 .01
-
The Diophantine Equation ax6 + by3 + cz2 = 0 in Gaussian In- tegers
Kyungpook Mathematical Journal
2015 .01
-
Goldbach-Linnik type problems with unequal powers of primes
대한수학회지
2022 .03
-
Some finiteness results for co-associated primes of generalized local homology modules and applications
대한수학회지
2020 .01
-
GENERALIZED FIBONACCI NUMBERS OF THE FORM 11x<sup>2</sup> + 1
호남수학학술지
2018 .01
-
The extendibility of Diophantine pairs with property $D(-1)$
한국수학논문집
2020 .01
-
More on the 2-prime ideals of commutative rings
대한수학회보
2020 .01
-
ON CARLESON'S INEQUALITY II
충청수학회지
2018 .01
-
On a Waring-Goldbach problem involving squares, cubes and biquadrates
대한수학회보
2018 .01
-
Continued fraction and Diophantine equation
대한수학회보
2016 .01
-
S(N)-almost prime submodules
Proceedings of the Jangjeon Mathematical Society
2019 .01
-
INEQUALITIES FOR INTEGRAL MEAN ESTIMATE OF POLYNOMIALS
Nonlinear Functional Analysis and Applications
2024 .03
-
SOME OPERATOR INEQUALITIES INVOLVING IMPROVED YOUNG AND HEINZ INEQUALITIES
순수 및 응용수학
2018 .01
-
ON THE EQUATION Φ(5m − 1) = 5ⁿ − 1
대한수학회보
2015 .01
-
SOME RESULTS ON ORDER PRIME GRAPHS AND GENERAL ORDER PRIME GRAPHS
Proceedings of the Jangjeon Mathematical Society
2021 .04
이 논문의 저자 정보
최근 본 자료
댓글(0)
0