| Résume | In this talk we report about our joint work with V. Kumar Murty andM. Manickam on the twisted averages of $L$-functions of integraland half integral weight modular forms. We show that given a halfintegral weight form $f$ of weight $k+1/2$, for sufficiently large primes$l$, a positive proportion of twists $L(f,\chi,k/2+1/4)$ by characters$\chi$ mod $l$ are non zero. This is not known in the case of integralweight forms. |
