Zobrazeno 1 - 10
of 52
pro vyhledávání: '"PRENDIVILLE, Sean"'
Autor:
Prendiville, Sean
We prove an effective version of the inverse theorem for the Gowers $U^3$-norm for functions supported on high-rank quadratic level sets in finite vector spaces. For configurations controlled by the $U^3$-norm (complexity-two configurations), this en
Externí odkaz:
http://arxiv.org/abs/2409.07962
A nonlinear version of Roth's theorem states that dense sets of integers contain configurations of the form $x$, $x+d$, $x+d^2$. We obtain a multidimensional version of this result, which can be regarded as a first step towards effectivising those ca
Externí odkaz:
http://arxiv.org/abs/2407.08338
Autor:
Ortega, Miquel, Prendiville, Sean
Generalising results of Erd\H{o}s-Freud and Lindstr\"om, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing that extremal Sidon sets are Fourier-pseudorando
Externí odkaz:
http://arxiv.org/abs/2110.13447
Autor:
ORTEGA, Miquel, PRENDIVILLE, Sean
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2023 Jan 01. 35(1), 115-134.
Externí odkaz:
https://www.jstor.org/stable/48728092
Autor:
Prendiville, Sean
We offer an alternative proof of a result of Conlon, Fox, Sudakov and Zhao on solving translation-invariant linear equations in dense Sidon sets. Our proof generalises to equations in more than five variables and yields effective bounds.
Comment
Comment
Externí odkaz:
http://arxiv.org/abs/2005.03484
Autor:
Prendiville, Sean
We show how to adapt the Hardy--Littlewood circle method to count monochromatic solutions to diagonal Diophantine equations. This delivers a lower bound which is optimal up to absolute constants. The method is illustrated on equations obtained by set
Externí odkaz:
http://arxiv.org/abs/2003.10161
Autor:
Peluse, Sarah, Prendiville, Sean
Publikováno v:
Int. Math. Res. Not. (2022), no. 8, 5658-5684
We show that sets of integers lacking the configuration $x$, $x+y$, $x+y^2$ have at most polylogarithmic density.
Comment: v2. Replaced use of Hahn-Banach theorem with simplified treatment involving Cauchy-Schwarz
Comment: v2. Replaced use of Hahn-Banach theorem with simplified treatment involving Cauchy-Schwarz
Externí odkaz:
http://arxiv.org/abs/2003.04122
Autor:
Prendiville, Sean
We give an exposition of the inverse theorem for the cut-norm associated to the nonlinear Roth configuration, established previously by Peluse and the author.
Comment: arXiv admin note: substantial text overlap with arXiv:1903.02592
Comment: arXiv admin note: substantial text overlap with arXiv:1903.02592
Externí odkaz:
http://arxiv.org/abs/2003.04121
Akademický článek
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Autor:
Chapman, Jonathan, Prendiville, Sean
We obtain a double exponential bound in Brauer's generalisation of van der Waerden's theorem, which concerns progressions with the same colour as their common difference. Such a result has been obtained independently and in much greater generality by
Externí odkaz:
http://arxiv.org/abs/1904.07567