Wyniki wyszukiwania

1

Small prime solutions of ternary linear equations

100%

Liu J., Tsang K.-M.

Acta Arithmetica

|

2005

|

tom 118

|

nr 1

79-100

2

Distribution of integers that are sums of three squares of primes

100%

Liu J., Zhan T.

Acta Arithmetica

|

2001

|

tom 98

|

nr 3

207-228

3

The ternary Goldbach problem in arithmetic progressions

100%

Liu J., Zhan T.

Acta Arithmetica

|

1997

|

tom 82

|

nr 3

197-227

EN

For a large odd integer N and a positive integer r, define b = (b₁,b₂,b₃) and $𝓑(N,r) = {b∈ ℕ³ : 1 ≤ b_j ≤ r, (b_j, r) = 1$ and b₁+b₂+b₃ ≡ N (mod r)}. It is known that $#𝓑(N,r) = r² ∏_{p|r}_{p|N} ((p-1)(p-2)/p²) ∏_{p|r}_{p∤N} ((p²-3p+3)/p²)$. Let ε > 0 be arbitrary and $R = N^{1/8-ε}$. We prove that for all positive integers r ≤ R, with at most $O(Rlog^{-A}N)$ exceptions, the Diophantine equation ⎧N = p₁+p₂+p₃, ⎨ $p_j ≡ b_j (mod r),$ j = 1,2,3,$ ⎩ with prime variables is solvable whenever b ∈ 𝓑(N,r), where A > 0 is arbitrary.

4

Distribution of zeros of Dirichlet L-functions and the least prime in an arithmetic progression

100%

Liu J., Ye Y.

Acta Arithmetica

|

2005

|

tom 119

|

nr 1

13-38

5

On sums of five almost equal prime squares

100%

Liu J., Zhan T.

Acta Arithmetica

|

1996

|

tom 77

|

nr 4

369-383

6

Four squares of primes and 165 powers of 2

100%

Liu J., Lü G.

Acta Arithmetica

|

2004

|

tom 114

|

nr 1

55-70

Ograniczanie wyników

6 Acta Arithmetica

6 Liu J.

3 Zhan T.

1 Lü G.

1 Tsang K.-M.

1 Ye Y.

2 2005

1 2004

1 2001

1 1997

1 1996

Small prime solutions of ternary linear equations

Distribution of integers that are sums of three squares of primes

The ternary Goldbach problem in arithmetic progressions

Distribution of zeros of Dirichlet L-functions and the least prime in an arithmetic progression

On sums of five almost equal prime squares

Four squares of primes and 165 powers of 2