We estimate weighted character sums with determinants ad-bc of 2×2 matrices modulo a prime p with entries a,b,c and d vary ing over the interval [1,N].Our goal is to obtain non-trivial bounds for values of N as s...We estimate weighted character sums with determinants ad-bc of 2×2 matrices modulo a prime p with entries a,b,c and d vary ing over the interval [1,N].Our goal is to obtain non-trivial bounds for values of N as small as possible.In particular,we achieve this goal,with a power saving,for N≥p^(1/8+ε) with any fixed ε>0,which is very likely to be the best possible unless the celebrated Burgess bound is improved,By other techniques,we also treat more general sums but sometimes for larger values of N.展开更多
基金supported in part by the Australian Research Council (Grant No. DP200100355)。
文摘We estimate weighted character sums with determinants ad-bc of 2×2 matrices modulo a prime p with entries a,b,c and d vary ing over the interval [1,N].Our goal is to obtain non-trivial bounds for values of N as small as possible.In particular,we achieve this goal,with a power saving,for N≥p^(1/8+ε) with any fixed ε>0,which is very likely to be the best possible unless the celebrated Burgess bound is improved,By other techniques,we also treat more general sums but sometimes for larger values of N.
