Zobrazeno 1 - 10
of 686
pro vyhledávání: '"Walsh, P N"'
Autor:
Walsh, Miguel N.
We introduce a strategy to tackle some known obstructions of current approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for intervals of length at least $(\log X)^{\psi(X)}$, with $\psi(X) \rightarrow \in
Externí odkaz:
http://arxiv.org/abs/2310.07873
Autor:
Walsh, Miguel N.
We develop tools to study the averaged Fourier uniformity conjecture and extend its known range of validity to intervals of length at least $\exp(C (\log X)^{1/2} (\log \log X)^{1/2})$.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2304.09792
Autor:
Walsh, Miguel N.
By associating frequencies to larger scales, we provide a simpler way to derive local uniformity of multiplicative functions on average from the results of Matom\"aki-Radziwill.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2102.05564
Autor:
Walsh, Miguel N.
We present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the method of
Externí odkaz:
http://arxiv.org/abs/1906.05843
Autor:
Walsh, Miguel N.
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties
Externí odkaz:
http://arxiv.org/abs/1811.07865
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent Bayesian approach
Externí odkaz:
http://arxiv.org/abs/1705.09395
Autor:
Walsh, Miguel N.
We establish the sharp estimate <<_d N^{2/d} for the number of rational points of height at most N on an irreducible projective curve of degree d. We deduce this from a result for general hypersurfaces that is sensitive to the coefficients of the cor
Externí odkaz:
http://arxiv.org/abs/1308.0574
Autor:
Walsh, Miguel N.
We show that every set S in [N]^d occupying less than p^t residue classes for some real number t < d and every prime p, must essentially lie in the solution set of a polynomial equation of degree at most (log N)^C, for some constant C depending only
Externí odkaz:
http://arxiv.org/abs/1307.0259
Autor:
Walsh, Miguel N.
We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L^2 norm.
Comment: 17 pages. Added further results and examples
Comment: 17 pages. Added further results and examples
Externí odkaz:
http://arxiv.org/abs/1109.2922
Autor:
Walsh, Miguel N.
Publikováno v:
Duke Math. J. 161, no. 10 (2012), 2001-2022
We show that if a big set of integer points in [0,N]^d, d>1, occupies few residue classes mod p for many primes p, then it must essentially lie in the solution set of some polynomial equation of low degree. This answers a question of Helfgott and Ven
Externí odkaz:
http://arxiv.org/abs/1105.1551