The origin of fast radio bursts ( FRBs ) still remains a mystery , even with the increased number of discoveries in the last three years .
Growing evidence suggests that some FRBs may originate from magnetars .
Large , single-dish telescopes such as Arecibo Observatory ( AO ) and Green Bank Telescope ( GBT ) have the sensitivity to detect FRB 121102-like bursts at gigaparsec distances .
Here we present searches using AO and GBT that aimed to find potential radio bursts at 11 sites of past \gamma –ray bursts that show evidence for the birth of a magnetar .
We also performed a search towards GW170817 , which has a merger remnant whose nature remains uncertain .
We place 10 \sigma fluence upper limits of \approx 0.036 Jy ms at 1.4 GHz and \approx 0.063 Jy ms at 4.5 GHz for AO data and fluence upper limits of \approx 0.085 Jy ms at 1.4 GHz and \approx 0.098 Jy ms at 1.9 GHz for GBT data , for a maximum pulse width of \approx 42 ms .
The AO observations had sufficient sensitivity to detect any FRB of similar luminosity to the one recently detected from the Galactic magnetar SGR 1935+2154 .
Assuming a Schechter function for the luminosity function of FRBs , we find that our non-detections favor a steep power–law index ( \alpha \lesssim - 1.0 ) and a large cut–off luminosity ( L _ { 0 } \gtrsim 10 ^ { 42 } erg/s ) .