AI 中文总结
该研究针对抛物线上的点，证明了度量丢番图逼近中Khintchine定理收敛情形的定量版本，核心是突破了逼近函数需单调的限制，还用到了Burgess界等经典数论结果。
AI 中文摘要
我们证明了度量丢番图逼近中著名的Khintchine定理收敛情形的定量版本，其中被逼近的点被限制在抛物线上。我们的结果的一个新特点是，与文献中的其他结果不同，逼近函数不再要求是单调的。这需要我们在经典数论结果中得到显式常数，最显著的是短区间内特征和的Burgess界。
英文摘要
We prove a quantitative version of the convergence case of Khintchine's celebrated theorem in metric Diophantine approximation, but where the approximated points are restricted to lying on the parabola. A novel feature of our result is that unlike other results in literature, the approximating function is no longer required to be monotonic. This requires us to obtain explicit constants in classical number theoretic results, most notably in Burgess' bound for character sums in short intervals.
Comments19 pages
