@article{215, abstract = {For any n≥3, let F ∈ Z[X0,...,Xn ] be a form of degree d *≥5 that defines a non-singular hypersurface X ⊂ Pn . The main result in this paper is a proof of the fact that the number N (F ; B) of Q-rational points on X which have height at most B satisfiesN (F ; B) = Od,ε,n (Bn −1+ε ), for any ε > 0. The implied constant in this estimate depends at most upon d, ε and n. New estimates are also obtained for the number of representations of a positive integer as the sum of three dth powers, and for the paucity of integer solutions to equal sums of like polynomials.*}, author = {Timothy Browning and Heath-Brown, Roger}, journal = {Bulletin of the London Mathematical Society}, number = {3}, pages = {401 -- 410}, publisher = {Wiley-Blackwell}, title = {{The density of rational points on non-singular hypersurfaces, I}}, doi = {10.1112/S0024609305018412}, volume = {38}, year = {2006}, } @article{216, abstract = {For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is concerned with the number Nz(B) of ℚ-rational points on Z which have height at most B. For any ε > 0, we establish the estimate NZ(B) = O d,ε,N(Bdim Z+ε), provided that d ≥ 6. As indicated, the implied constant depends at most on d, ε, and N.}, author = {Timothy Browning and Heath-Brown, Roger and Salberger, Per}, journal = {Duke Mathematical Journal}, number = {3}, pages = {545 -- 578}, publisher = {Unknown}, title = {{Counting rational points on algebraic varieties}}, doi = {10.1215/S0012-7094-06-13236-2}, volume = {132}, year = {2006}, } @article{218, abstract = {This paper is concerned with the average order of certain arithmetic functions, as they range over the values taken by binary forms.}, author = {de la Bretèche, Régis and Timothy Browning}, journal = {Acta Arithmetica}, number = {3}, pages = {291 -- 304}, publisher = {Instytut Matematyczny}, title = {{Sums of arithmetic functions over values of binary forms}}, doi = {10.4064/aa125-3-6}, volume = {125}, year = {2006}, } @inproceedings{2333, author = {Lieb, Élliott H and Robert Seiringer and Solovej, Jan P}, pages = {239 -- 248}, publisher = {American Mathematical Society}, title = {{Ground-state energy of a dilute Fermi gas}}, doi = {10.1090/conm/412}, volume = {412}, year = {2006}, } @inproceedings{2334, author = {Robert Seiringer and Lieb, Élliott H and Yngvason, Jakob}, editor = {Zambrini, Jean-Claude}, publisher = {World Scientific Publishing}, title = {{One-dimensional behavior of dilute, trapped Bose gases in traps}}, doi = {10.1007/s00220-003-0993-3}, year = {2006}, }