Measurement of the Photon Structure Function at High Q 2 at LEP

The structure functions of real and virtual photons are derivedfrom cross section measurements of the reaction$\rm e^+e^-\rightarrow e^+e^- + \hbox{hadrons}$ at LEP.The reaction is studied at $\sqrt{\rm {s}} \simeq 91$ GeV with the L3detector. One of the final state electrons is detected at a large angle relative to the beam direction, leading to $Q^2$ values between40 GeV$^2$ and 500 GeV$^2$.The other final state electron is either undetected or it is detected ata four- momentum transfersquared $P^2$ between 1 GeV$^2$ and 8 GeV$^2$.These measurements are compared with predictions of the Quark PartonModel and other QCD based models.