We obtain bounds on the average size of Bohr sets with coefficients parametrised by polynomials over finite fields and obtain a series of general results and also some sharper results for specific sets which are important for applications to computer science. In particular, we use our estimates to show that a heuristic assumption used in the many variable version of Coppersmith's method holds with high probability. We demonstrate the use of our results on the approximate greatest common divisor problem and obtain a fully rigorous version of the heuristic algorithm of H. Cohn and N. Heninger (2013).

翻译：我们得到了有限域上由多项式参数化系数的Bohr集平均大小的界，获得了一系列一般性结果，并对计算机科学应用中重要的特定集合给出了更精确的结论。特别地，我们利用这些估计证明了多变量Coppersmith方法中使用的启发式假设以高概率成立。我们展示了这些结果在近似最大公因子问题上的应用，并得到了H. Cohn与N. Heninger (2013) 启发式算法的完全严格化版本。