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pro vyhledávání: '"Browning T"'
Autor:
Browning, T. D., Hu, L. Q.
An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski open subset of an arbitrary smooth biquadratic hypersurface in sufficiently many variables. The proof uses the Hardy
Externí odkaz:
http://arxiv.org/abs/1810.08426
Autor:
Browning, T. D., Heath-Brown, D. R.
Publikováno v:
Duke Math. J. 169, no. 16 (2020), 3099-3165
An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface $x_1y_1^2+\dots+x_4y_4^2=0$ in $\mathbb{P}^3\times\mathbb{P}^3$. This
Externí odkaz:
http://arxiv.org/abs/1805.10715
Autor:
Browning, T. D., Heath-Brown, D. R.
Publikováno v:
Discrete Analysis 2018:15
We give an upper bound for the number of rational points of height at most $B$, lying on a surface defined by a quadratic form $Q$. The bound shows an explicit dependence on $Q$. It is optimal with respect to $B$, and is also optimal for typical form
Externí odkaz:
http://arxiv.org/abs/1801.00979
Autor:
Browning, T. D., Sofos, E.
For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with integer coeffic
Externí odkaz:
http://arxiv.org/abs/1706.04331
Autor:
Browning, T. D.
Publikováno v:
Mathematika 63 (2017) 818-839
Building on recent work of Bhargava--Elkies--Schnidman and Kriz--Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain rational points.
Comment: 23 pages; minor edits and added new remark (R
Comment: 23 pages; minor edits and added new remark (R
Externí odkaz:
http://arxiv.org/abs/1701.00525
Autor:
Browning, T. D., Sofos, E.
Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over $\mathbb{Q}$ that contains a conic defined over $\mathbb{Q}$.
Comment: 39 pages, t
Comment: 39 pages, t
Externí odkaz:
http://arxiv.org/abs/1609.09057
We show that a twisted variant of Linnik's conjecture on sums of Kloosterman sums leads to an optimal covering exponent for $S^3$.
Comment: 23 pages
Comment: 23 pages
Externí odkaz:
http://arxiv.org/abs/1609.06097
Autor:
Browning, T. D., Gorodnik, A.
Given a symmetric variety Y defined over the rationals and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of i
Externí odkaz:
http://arxiv.org/abs/1606.06342
Publikováno v:
Compositio Math. 152 (2016) 1435-1475
Given a family of varieties $X\to \mathbb{P}^n$ over a number field $k$, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for $100\%$ of the fibres which are everywhere locally soluble.
Comment: 44 pa
Comment: 44 pa
Externí odkaz:
http://arxiv.org/abs/1506.01817
Autor:
Browning, T. D., Heath-Brown, D. R.
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and
Externí odkaz:
http://arxiv.org/abs/1403.5937