Assume the Riemann Hypothesis and a weaker form of Montgomery's pair correlation conjecture, i.e., for every $\theta\in[1,2)$ $$F(X,T)=4\sum_{0<\gamma_1,\gamma_2\leq T}\frac{X^{i(\gamma_1-\gamma_2)}}{4+(\gamma_1-\gamma_2)^2} \ll T(\log T)^\theta,$$ where $\gamma_j$, $j=1,2$, run over the imaginary part of the non-trivial zeros of the Riemann zeta-function, holds uniformly for $\frac{X}{H}\leq T\leq X$, where $1\leq H \leq X$. Then, for all sufficiently large $X$ and $H\gg (\log X)^\theta$, we have that the interval $[X,X+H]$ contains a even integer which is a sum of two primes.
A conditional result on Goldbach numbers in short intervals
LANGUASCO, ALESSANDRO
1998
Abstract
Assume the Riemann Hypothesis and a weaker form of Montgomery's pair correlation conjecture, i.e., for every $\theta\in[1,2)$ $$F(X,T)=4\sum_{0<\gamma_1,\gamma_2\leq T}\frac{X^{i(\gamma_1-\gamma_2)}}{4+(\gamma_1-\gamma_2)^2} \ll T(\log T)^\theta,$$ where $\gamma_j$, $j=1,2$, run over the imaginary part of the non-trivial zeros of the Riemann zeta-function, holds uniformly for $\frac{X}{H}\leq T\leq X$, where $1\leq H \leq X$. Then, for all sufficiently large $X$ and $H\gg (\log X)^\theta$, we have that the interval $[X,X+H]$ contains a even integer which is a sum of two primes.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
[4].pdf
accesso aperto
Tipologia:
Published (publisher's version)
Licenza:
Accesso gratuito
Dimensione
461.66 kB
Formato
Adobe PDF
|
461.66 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.