@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},
}
@article{6835,
abstract = {We derive the Hasse principle and weak approximation for fibrations of certain varieties in the spirit of work by Colliot-Thélène–Sansuc and Harpaz–Skorobogatov–Wittenberg. Our varieties are defined through polynomials in many variables and part of our work is devoted to establishing Schinzel's hypothesis for polynomials of this kind. This last part is achieved by using arguments behind Birch's well-known result regarding the Hasse principle for complete intersections with the notable difference that we prove our result in 50% fewer variables than in the classical Birch setting. We also study the problem of square-free values of an integer polynomial with 66.6% fewer variables than in the Birch setting.},
author = {Destagnol, Kevin N and Sofos, Efthymios},
issn = {0007-4497},
journal = {Bulletin des Sciences Mathematiques},
publisher = {Elsevier},
title = {{Rational points and prime values of polynomials in moderately many variables}},
doi = {10.1016/j.bulsci.2019.102794},
volume = {156},
year = {2019},
}