The dispersion of the E_ p,i--L_ iso correlation of long gamma--ray bursts is partially due to assembling different sources

We found a mistake in the code used to compute the param-1 eters m, q, and σ int of the E p,i -L iso and E p,i -L coll correlations 2 reported in Tables 1,2, and 3. We verified to see whether the 3 essence of our results remains unaffected, and in fact the statis-4 tical evidence of our conclusions is even stronger than what was 5 reported in the Letter.6 For each burst in the sample, we recomputed the aforemen-7 tioned parameters and provide the correct values in Tables 1, 2, 8 and 3, which are meant to replace those reported in the Letter.We 9 also provide the amended version of Fig. 1.Not only do the gen-10 eral conclusions that we found remain valid, but the main result 11 shown in Sect.3.1 improved.