| Abstract: | Let f1(x1,..., xl1) and f2(y1,...,yl2) be positive definite primitive quadratic forms in l1 and l2 variables, respectively. We obtain new results in the well-known problem on the number of lattice points on the cone f1(x1,...,xl1)=f2(y1,...,yl2), in the domain f1(x1,...,xl1)≦N for N»∞. Our technical tool is the Rankin-Selberg convolution. In several special cases the results can be sharpened by other methods. In addition, new facts concerning the uniform distribution of lattice points on ellipsoids in l variables, l odd, l≧5 are obtained. |
