Elaborating on Katzel's result, Zhai obtained a sharp short interval result for the number of ways of expressing a square-free integer as sums of two squares. In this note we view Zhai's decom- position as one by de...Elaborating on Katzel's result, Zhai obtained a sharp short interval result for the number of ways of expressing a square-free integer as sums of two squares. In this note we view Zhai's decom- position as one by degree 1 prime ideals in the Gaussian field and extend Zhai's approach to a wider range of quadratic fields etc.展开更多
基金supported in part by JSPS (Grant No. 17540050)supported in part by China NNSF (Grant No. 10726051)Grant in-aid for Scientific Research from Department of Mathematics, Jilin University
文摘Elaborating on Katzel's result, Zhai obtained a sharp short interval result for the number of ways of expressing a square-free integer as sums of two squares. In this note we view Zhai's decom- position as one by degree 1 prime ideals in the Gaussian field and extend Zhai's approach to a wider range of quadratic fields etc.
基金Supported by Graduate Independent Innovation Foundation of Northwest University(YZZ12061)Scientific Research Program Funded by Shaanxi Provincial Education Department(2013JK0562)