Pair Correlation of Zeros and Primes in Short Intervals
Pair Correlation of Zeros and Primes in Short Intervals
复制标题
短区间内零点和素数的配对相关性
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
H. Montgomery
中科院分区：
文献类型：
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作者：
D. Goldston;H. Montgomery
In 1943, A. Selberg [15] Deduced From The Riemann Hypothesis (Rh) that
$$intlimits_{
m{1}}^{
m{X}} {{{left( {psi left( {left( {{
m{1 + }}delta }
ight){
m{x}}}
ight){
m{ - }}psi left( {
m{x}}
ight){
m{ - }}delta {
m{x}}}
ight)}^2}{{
m{x}}^{{
m{ - 2}}}}{
m{dx}} ll delta {{left( {{mathop{
m l}
olimits} {
m{ogX}}}
ight)}^2}}$$
(1)
for X–1 ≤ δ ≤ X–1/4, X ≥ 2. Selberg was concerned with small values of δ and the constraint δ ≤ X–1/4 was imposed more for convenience than out of necessity. For Larger δ we have the following result.
In 1943, A. Selberg [15] Deduced From The Riemann Hypothesis (Rh) that
$$intlimits_{
m{1}}^{
m{X}} {{{left( {psi left( {left( {{
m{1 + }}delta }
ight){
m{x}}}
ight){
m{ - }}psi left( {
m{x}}
ight){
m{ - }}delta {
m{x}}}
ight)}^2}{{
m{x}}^{{
m{ - 2}}}}{
m{dx}} ll delta {{left( {{mathop{
m l}
olimits} {
m{ogX}}}
ight)}^2}}$$
(1)
for X–1 ≤ δ ≤ X–1/4, X ≥ 2. Selberg was concerned with small values of δ and the constraint δ ≤ X–1/4 was imposed more for convenience than out of necessity. For Larger δ we have the following result.