This article presents the results of a study on the spectral and energetic properties of twelve gamma-ray bursts (GRBs) with known redshifts, detected by the BeppoSAX satellite. The study focuses on the intrinsic spectra and energetics of these GRBs in their cosmological rest frames. The GRBs were observed across a broad energy range (2–700 keV) and their spectra were well described by the Band model, with no significant soft X-ray excesses or spectral absorptions. The study found a positive correlation between the estimated total isotropic energy $E_{rad}$ in the 1–10000 keV range and redshift $z$. Additionally, more luminous GRBs were characterized by larger peak energies $E_{p,s}$ of their $EF(E)$ spectra. More distant GRBs were systematically harder in the X-ray band compared to those with lower redshifts. The study also discusses possible selection and data truncation effects that could bias the results and provides possible explanations for the observed correlations. The GRB sample includes twelve events with reliable redshift estimates, obtained from optical emission lines in the spectra of their host galaxies or from other methods such as photometric data or X-ray afterglow spectra. The study used the BeppoSAX GRBM and WFC detectors to analyze the spectra of these GRBs. The spectral analysis was performed using the Band model, which describes the spectra as a smoothly broken power-law. The study also computed the total radiated energy $E_{rad}$ of each GRB, taking into account the cosmological redshift and the luminosity distance. The results show that the intrinsic X-ray and gamma-ray durations do not show significant correlations with redshift. The study found a correlation between the low-energy photon index $\alpha$ and redshift, as well as between $E_p$ and $E_{rad}$. The correlation between $\alpha$ and $E_{rad}$ was found to be weaker. The study also found that the correlation between $E_p$ and $E_{rad}$ is stronger than the correlation between $\alpha$ and $E_{rad}$, with the former being more significant. The study also found that the correlation between $log|\alpha|$ and $log(1 + z)$ is strong, as is the correlation between $logE_p$ and $logE_{rad}$. The study discusses possible explanations for the observed correlations, including the possibility that the observed correlations are due to the intrinsic properties of the population of long GRBs, which are brighter and more energetic at larger distances. The study also notes that the observed correlations are not due to selection effects or data truncation, as the sample is representative of the overall GRB population. The study concludes that the observed correlations are likely due to the intrinsic properties of the GRB population. The study also finds that the peak energy $E_p$ of GRBs is proportionalThis article presents the results of a study on the spectral and energetic properties of twelve gamma-ray bursts (GRBs) with known redshifts, detected by the BeppoSAX satellite. The study focuses on the intrinsic spectra and energetics of these GRBs in their cosmological rest frames. The GRBs were observed across a broad energy range (2–700 keV) and their spectra were well described by the Band model, with no significant soft X-ray excesses or spectral absorptions. The study found a positive correlation between the estimated total isotropic energy $E_{rad}$ in the 1–10000 keV range and redshift $z$. Additionally, more luminous GRBs were characterized by larger peak energies $E_{p,s}$ of their $EF(E)$ spectra. More distant GRBs were systematically harder in the X-ray band compared to those with lower redshifts. The study also discusses possible selection and data truncation effects that could bias the results and provides possible explanations for the observed correlations. The GRB sample includes twelve events with reliable redshift estimates, obtained from optical emission lines in the spectra of their host galaxies or from other methods such as photometric data or X-ray afterglow spectra. The study used the BeppoSAX GRBM and WFC detectors to analyze the spectra of these GRBs. The spectral analysis was performed using the Band model, which describes the spectra as a smoothly broken power-law. The study also computed the total radiated energy $E_{rad}$ of each GRB, taking into account the cosmological redshift and the luminosity distance. The results show that the intrinsic X-ray and gamma-ray durations do not show significant correlations with redshift. The study found a correlation between the low-energy photon index $\alpha$ and redshift, as well as between $E_p$ and $E_{rad}$. The correlation between $\alpha$ and $E_{rad}$ was found to be weaker. The study also found that the correlation between $E_p$ and $E_{rad}$ is stronger than the correlation between $\alpha$ and $E_{rad}$, with the former being more significant. The study also found that the correlation between $log|\alpha|$ and $log(1 + z)$ is strong, as is the correlation between $logE_p$ and $logE_{rad}$. The study discusses possible explanations for the observed correlations, including the possibility that the observed correlations are due to the intrinsic properties of the population of long GRBs, which are brighter and more energetic at larger distances. The study also notes that the observed correlations are not due to selection effects or data truncation, as the sample is representative of the overall GRB population. The study concludes that the observed correlations are likely due to the intrinsic properties of the GRB population. The study also finds that the peak energy $E_p$ of GRBs is proportional