@article{2407,
abstract = {Two definitions of the effective mass of a particle interacting with a quantum field, such as a polaron, are considered and shown to be equal in models similar to the Fröhlich polaron model. These are: 1. the mass defined by the low momentum energy E(P)≈E(0)+P2/2 M of the translation invariant system constrained to have momentum P and 2. the mass M of a simple particle in an arbitrary slowly varying external potential, V, described by the nonrelativistic Schrödinger equation, whose ground state energy equals that of the combined particle/field system in a bound state in the same V.},
author = {Lieb, Élliott and Seiringer, Robert},
journal = {Journal of Statistical Physics},
number = {1-2},
pages = {51 -- 57},
publisher = {Springer},
title = {{Equivalence of two definitions of the effective mass of a polaron}},
doi = {10.1007/s10955-013-0791-z},
volume = {154},
year = {2014},
}
@article{248,
abstract = {For any pencil of conics or higher-dimensional quadrics over ℚ, with all degenerate fibres defined over ℚ, we show that the Brauer–Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics over ℚ, which is a consequence of recent advances in additive combinatorics.},
author = {Timothy Browning and Matthiesen, Lilian and Skorobogatov, Alexei N},
journal = {Annals of Mathematics},
number = {1},
pages = {381 -- 402},
publisher = {John Hopkins University Press},
title = {{Rational points on pencils of conics and quadrics with many degenerate fibres}},
doi = {https://doi.org/10.4007/annals.2014.180.1.8},
volume = {180},
year = {2014},
}
@article{249,
abstract = {A version of the Hardy-Littlewood circle method is developed for number fields K/ℚ and is used to show that nonsingular projective cubic hypersurfaces over K always have a K-rational point when they have dimension at least 8. },
author = {Timothy Browning and Vishe, Pankaj},
journal = {Duke Mathematical Journal},
number = {10},
pages = {1825 -- 1883},
publisher = {Duke University Press},
title = {{Cubic hypersurfaces and a version of the circle method for number fields}},
doi = {10.1215/00127094-2738530},
volume = {163},
year = {2014},
}
@article{252,
abstract = {For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.},
author = {Timothy Browning and Jones, Michael S},
journal = {Acta Arithmetica},
number = {3},
pages = {271 -- 298},
publisher = {Instytut Matematyczny},
title = {{Counting rational points on del Pezzo surfaces with a conic bundle structure}},
doi = {10.4064/aa163-3-6},
volume = {163},
year = {2014},
}
@article{254,
abstract = {A new "polynomial sieve" is presented and used to show that almost all integers have at most one representation as a sum of two values of a given polynomial of degree at least 3.},
author = {Timothy Browning},
journal = {International Mathematics Research Notices},
number = {7},
pages = {1987 -- 2019},
publisher = {Oxford University Press},
title = {{The polynomial sieve and equal sums of like polynomials}},
doi = {10.1093/imrn/rnt350},
volume = {2015},
year = {2014},
}