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Salem Sets with No Arithmetic Progressions
(Oxford University Press, 2017-04)
We construct compact Salem sets in R/Z of any dimension (including 1), which do not contain any arithmetic progressions of length 3. Moreover, the sets can be taken to be Ahlfors regular if the dimension is less than 1, ...
Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
(Birkhauser Boston Inc, 2021-02)
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real line which avoid ε-approximations of arithmetic progressions. Some of these estimates are in terms of Szemerédi bounds. In ...
The least prime in certain arithmetic progressions
(Mathematical Association of America, 2009-12)
Dirichlet’s theorem states that, if a and n are relatively prime integers, there are infinitely many primes in the arithmetic progression n + a, 2n + a, 3n + a,.... However, the known proofs of this general result are not ...
Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
(Public Library of Science, 2016-12)
We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the ...
On a paper of Dressler and Van de Lune
(Springer, 2020-11-19)
If z∈ C and 1 ≤ n is a natural number then ∑d1d2=n(1-zp1)⋯(1-zpm)zq1e1+⋯+qiei=1, where d1=p1r1⋯pmrm, d2=q1e1⋯qiei are the prime decompositions of d1, d2. This is one of the identities involving arithmetic functions that ...
When order matters: Last-come first-served effect in sequential arithmetic operations
(Imperial College Press, 2012-11)
Cognitive psychologists have relied on dual-task interference experiments to understand the low-capacity and serial nature of conscious mental operations. Two widely studied paradigms, the Attentional Blink (AB) and the ...
The inverse Sieve problem in high dimensions
(Duke University Press, 2012-07)
We show that if a big set of integer points S ⊆ [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 ...
Desarrollo de la memoria de trabajo y desempeño en cálculo aritmético: Un estudio longitudinal en niñosDevelopment of working memory and performance in arithmetic: a longitudinal study with children
(Universidad de Almería, 2014-04)
Introducción. Este estudio ha tenido por objetivo investigar la relación entre el desarrollo de la memoria de trabajo y el desempeño en actividades aritméticas. Método. Se realizó un estudio longitudinal con una muestra ...
Group arithmetic in c-3,c-5 curvesJOURNAL OF SYMBOLIC COMPUTATIONJ SYMB COMPUT
(ACADEMIC PRESS, 2013)