Add to ORKGWe use recent results about linking the number of zeros on algebraic varieties over $\mathbb{C}$, defined by polynomials with integer coefficients, and on their reductions modulo sufficiently large primes to study congruences with products and reciprocals of linear forms. This allows us to make some progress towards a question of B. Murphy, G. Petridis, O. Roche-Newton, M. Rudnev and I. D. Shkredov (2019) on an extreme case of the Erd\H{o}s-Szemer\'{e}di conjecture in finite fields.Comment: Corrected an error in the previous version and added a stronger result which holds for almost all prime
In this paper, we strengthen a result by Green about an analogue of Sarkozy's theorem in the setting...
In this thesis, we investigate various topics regarding the arithmetic of polynomials over finite fi...
AbstractLet g be an element of order T over a finite field Fp of p elements, where p is a prime. We ...
Products of Differences over Arbitrary Finite Fields, Discrete Analysis 2018:18, 42 pp. A central p...
The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many prod...
In our paper, we introduce a new method for estimating incidences via representation theory. We obta...
We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rat...
This is a survey on sum-product formulae and methods. We state old and new results. Our main objecti...
AbstractWe study a Szemerédi–Trotter type theorem in finite fields. We then use this theorem to obta...
We prove finiteness results on integral points on complements of large divisors in projective variet...
We give some estimates for multiplicative character sums on quasiprojective varieties over finite f...
In this paper, we establish some finiteness results about the multiplicative dependence of rational ...
We prove finiteness results for sets of varieties over number fields with good reduction outside a g...
We give a complete conjectural formula for the number er(d, m) of maximum possible Fq-rational point...
The thesis starts with two expository chapters. In the first one we discuss abelian varieties with p...
In this paper, we strengthen a result by Green about an analogue of Sarkozy's theorem in the setting...
In this thesis, we investigate various topics regarding the arithmetic of polynomials over finite fi...
AbstractLet g be an element of order T over a finite field Fp of p elements, where p is a prime. We ...
Products of Differences over Arbitrary Finite Fields, Discrete Analysis 2018:18, 42 pp. A central p...
The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many prod...
In our paper, we introduce a new method for estimating incidences via representation theory. We obta...
We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rat...
This is a survey on sum-product formulae and methods. We state old and new results. Our main objecti...
AbstractWe study a Szemerédi–Trotter type theorem in finite fields. We then use this theorem to obta...
We prove finiteness results on integral points on complements of large divisors in projective variet...
We give some estimates for multiplicative character sums on quasiprojective varieties over finite f...
In this paper, we establish some finiteness results about the multiplicative dependence of rational ...
We prove finiteness results for sets of varieties over number fields with good reduction outside a g...
We give a complete conjectural formula for the number er(d, m) of maximum possible Fq-rational point...
The thesis starts with two expository chapters. In the first one we discuss abelian varieties with p...
In this paper, we strengthen a result by Green about an analogue of Sarkozy's theorem in the setting...
In this thesis, we investigate various topics regarding the arithmetic of polynomials over finite fi...
AbstractLet g be an element of order T over a finite field Fp of p elements, where p is a prime. We ...