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}
}```
• D. R. Heath-Brown
• Published 1996
• Mathematics
• Journal für die reine und angewandte Mathematik (Crelles Journal)
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…
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