@article{175,
abstract = {An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points.},
author = {Browning, Timothy D and Loughran, Daniel},
issn = {10886850},
journal = {Transactions of the American Mathematical Society},
number = {8},
pages = {5757--5785},
publisher = {American Mathematical Society},
title = {{Sieving rational points on varieties}},
volume = {371},
year = {2019},
}
@article{6310,
abstract = {An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariskiopen subset of an arbitrary smooth biquadratic hypersurface in sufficiently many variables. The proof uses the Hardy–Littlewood circle method.},
author = {Browning, Timothy D and Hu, L.Q.},
issn = {10902082},
journal = {Advances in Mathematics},
pages = {920--940},
publisher = {Elsevier},
title = {{ Counting rational points on biquadratic hypersurfaces}},
doi = {10.1016/j.aim.2019.04.031},
volume = {349},
year = {2019},
}
@article{6620,
abstract = {This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of ℙ3ℚ given by the following equation 𝑥0(𝑥21+𝑥22)−𝑥33=0 in agreement with the Manin-Peyre conjectures.
},
author = {De La Bretèche, Régis and Destagnol, Kevin N and Liu, Jianya and Wu, Jie and Zhao, Yongqiang},
issn = {16747283},
journal = {Science China Mathematics},
publisher = {Springer},
title = {{On a certain non-split cubic surface}},
doi = {10.1007/s11425-018-9543-8},
year = {2019},
}