Let n linear forms Li on m variables be given, normalized so that all coefficients have absolute value at most unity. Let w1, ..., wm be real numbers and x1, ..., xm be integers. We say Ei= Li (w1, ..., wm)- Li (x1, ..., xm) is the error in approximating the w's by the x's with respect to form Li It is shown that given any w's there is an integral approximation of x's so that the errors Ei are small-roughly that(Formula presented.) simultaneously for all i.
All Science Journal Classification (ASJC) codes
- Hadamard Matrix
- Integral Approximation
- Pigeonhole Principle
- Probabilistic Method