On a hybrid bound for twisted L-values

摘要

Let f ∈S _k (M, ψ) be a newform, and let χ be a primitive character of conductor q. We express L(frac12+it,fÄc){L(frac{1}{2}+it,fotimeschi)} as a short combination of bilinear forms involving Kloosterman fractions. Using this we establish the convexity breaking bound L(tfrac12+it,fÄc) < 0.