# A new form of the circle method, and its application to quadratic forms.

@article{HeathBrown1996ANF, title={A new form of the circle method, and its application to quadratic forms.}, author={D. R. Heath-Brown}, journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)}, year={1996}, volume={1996}, pages={149 - 206} }

If the coefficients r(n) satisfy suitable arithmetic conditions the behaviour of F (α) will be determined by an appropriate rational approximation a/q to α, with small values of q usually producing large values of F (α). When α lies in an interval [a/q − δ, a/q + δ] with q small, a ‘major arc’, one hopes to estimate F (α) asymptotically, while if the corresponding q is large, for the ‘minor arcs’, one hopes that F (α) will be small, at least on average. One can distinguish two different types…

## 154 Citations

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