Related papers: Primitive recursive bounds for the finite version …

This paper gives the first quantitative bounds for the inverse theorem for the Gowers $U^4$-norm over $\mathbb{F}_p^n$ when $p=2,3$. We build upon earlier work of Gowers and Mili\'cevi\'c who solved the corresponding problem for $p\geq 5$.…

We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals, and then apply them to proving primitive recursiveness of some natural problems in linear algebra and analysis. In…

We provide a new proof of the inverse theorem for the Gowers $U^{s+1}$-norm over groups $H=\mathbb Z/N\mathbb Z$ for $N$ prime. This proof gives reasonable quantitative bounds (the worst parameters are double-exponential), and in particular…

Spencer asked whether the Paris-Harrington version of the Folkman-Sanders theorem has primitive recursive upper bounds. We give a positive answer to this question.

We establish quantitative bounds on the $U^k[N]$ Gowers norms of the M\"obius function $\mu$ and the von Mangoldt function $\Lambda$ for all $k$, with error terms of shape $O((\log\log N)^{-c})$. As a consequence, we obtain quantitative…

Positivity bounds are theoretical constraints on the Wilson coefficients of an effective field theory. These bounds emerge from the requirement that a given effective field theory must be the low-energy limit of a relativistic quantum…

We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…

We give a lower bound on multiplicative orders of some elements in defined by Conway towers of finite fields of characteristic two and also formulate a condition under that these elements are primitive

We prove the so-called inverse conjecture for the Gowers U^{s+1}-norm in the case s = 3 (the cases s < 3 being established in previous literature). That is, we establish that if f : [N] -> C is a function with |f(n)| <= 1 for all n and || f…

In this article we generalize Cobham theorem to a large class of substitutions including non primitive and non constant length substitutions.

We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here.

We show that the infinite-dimensional versions of Gowers' $\mathrm{FIN}_k$ and $\mathrm{FIN}_{\pm k}$ theorems can be parametrized by an infinite sequence of perfect subsets of $2^\omega$. To do so, we use ultra-Ramsey theory to obtain…

We study the primitive recursive analogue of computable categoricity spectra for various natural classes of structures. We show that these notions coincide for all relatively $\Delta_{2}^{0}$-categorical equivalence structures and linear…

We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…

We provide an explicit characterization of the properties of primitive recursive functions that are decidable or semi-decidable, given a primitive recursive index for the function. The result is much more general as it applies to any c.e.…

Extending a classical estimate of Mertens for the sum of the reciprocals of the first primes, we provide an explicit remainder formula for products of an arbitrary, but fixed, number of primes.

Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.

We develop a complex differential geometric approach to the theory of higher residues and primitive forms from the viewpoint of Kodaira-Spencer gauge theory, unifying the semi-infinite period maps for Calabi-Yau models and Landau-Ginzburg…

In this note we classify the primitive ideals in finite W-algebras of type A.

We construct a recursive formula for a complete system of primitive orthogonal idempotents for any $R$-trivial monoid. This uses the newly proved equivalence between the notions of $R$-trivial monoid and weakly ordered monoid.