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1
Content available remote

The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes (II)

100%
Li H.
Acta Arithmetica
|
2000-2001
|
tom 96
|
nr 4
369-379
2
Content available remote

The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes

100%
Li H.
Acta Arithmetica
|
2000
|
tom 92
|
nr 3
229-237
3
Content available remote

Representation of odd integers as the sum of one prime, two squares of primes and powers of 2

100%
Li H.
Acta Arithmetica
|
2007
|
tom 128
|
nr 3
223-233
4
Content available remote

Diagonal cubic equations

100%
Li H.
Acta Arithmetica
|
1997
|
tom 81
|
nr 3
199-227
5
Content available remote

A hybrid of theorems of Goldbach and Piatetski-Shapiro

100%
Li H.
Acta Arithmetica
|
2003
|
tom 107
|
nr 4
307-326
6
Content available remote

The exceptional set of Goldbach numbers (II)

100%
Li H.
Acta Arithmetica
|
2000
|
tom 92
|
nr 1
71-88
EN
1. Introduction. A positive number which is a sum of two odd primes is called a Goldbach number. Let E(x) denote the number of even numbers not exceeding x which cannot be written as a sum of two odd primes. Then the Goldbach conjecture is equivalent to proving that E(x) = 2 for every x ≥ 4. E(x) is usually called the exceptional set of Goldbach numbers. In [8] H. L. Montgomery and R. C. Vaughan proved that $E(x) = O(x^{1-Δ})$ for some positive constant Δ > 0$. In [3] Chen and Pan proved that one can take Δ >0.01. In [6], we proved thatE(x) = O(x^{0.921})$. In this paper we prove the following result. Theorem. For sufficiently large x, $E(x) =O (x^{0.914})$. Throughout this paper, ε always denotes a sufficiently small positive number that may be different at each occurrence. A is assumed to be sufficiently large, A < Y, and $D = Y^{1+ε}$.
7
Content available remote

Sums of one prime and two prime squares

100%
Li H.
Acta Arithmetica
|
2008
|
tom 134
|
nr 1
1-9
8
Content available remote

Small prime solutions of linear ternary equations

88%
Li H.
Acta Arithmetica
|
2001
|
tom 98
|
nr 3
293-309
9
Content available remote

Four prime squares and powers of 2

88%
Li H.
Acta Arithmetica
|
2006
|
tom 125
|
nr 4
383-391
10
Content available remote

The Romanoff theorem revisited

64%
Li H., Pan H.
Acta Arithmetica
|
2008
|
tom 135
|
nr 2
137-142
11
Content available remote

Difference sets and polynomials of prime variables

64%
Li H., Pan H.
Acta Arithmetica
|
2009
|
tom 138
|
nr 1
25-52
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