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pro vyhledávání: '"Shparlinski Igor E."'
Recently there has been several works estimating the number of $n\times n$ matrices with elements from some finite sets $\mathcal X$ of arithmetic interest and of a given determinant. Typically such results are compared with the trivial upper bound $
Externí odkaz:
http://arxiv.org/abs/2408.04350
Autor:
Ostafe, Alina, Shparlinski, Igor E.
Towards a well-known open question in arithmetic dynamics, L. M\'erai, A. Ostafe and I. E. Shparlinski (2023), have shown, for a class of polynomials $f \in \mathbb Z[X]$, which in particular includes all quadratic polynomials, that, under some natur
Externí odkaz:
http://arxiv.org/abs/2407.20464
Autor:
Shparlinski, Igor E.
We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). The improvement is based on exploiting the trilinear structure of certain exponential sums, appearing in the argument
Externí odkaz:
http://arxiv.org/abs/2404.10278
We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between Farey fra
Externí odkaz:
http://arxiv.org/abs/2404.09295
We consider Artin's conjecture on primitive roots over a number field $K$, reducing an algebraic number $\alpha\in K^\times$. Under the Generalised Riemann Hypothesis, there is a density ${\mathrm{dens}}(\alpha)$ counting the proportion of the primes
Externí odkaz:
http://arxiv.org/abs/2401.11589
We consider the set of $n\times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matrices of a given rank and then apply them to count such matrices with a
Externí odkaz:
http://arxiv.org/abs/2401.10086
Autor:
Ostafe, Alina, Shparlinski, Igor E.
We consider the set $\mathcal M_n(\mathbb Z; H)$ of $n\times n$-matrices with integer elements of size at most $H$ and obtain upper bounds on the number of matrices from $\mathcal M_n(\mathbb Z; H)$, for which the characteristic polynomial has a fixe
Externí odkaz:
http://arxiv.org/abs/2312.12626
Autor:
Shparlinski, Igor E.
We use bounds on bilinear forms with Kloosterman fractions and improve the error term in the asymptotic formula of Balazard and Martin (2023) on the average value of the smallest denominators of rational numbers in short intervals.
Externí odkaz:
http://arxiv.org/abs/2311.16640
Autor:
Mérai, László, Shparlinski, Igor E.
We consider the set $\mathcal{M}_n(\mathbb{Z}; H)$ of $n\times n$-matrices with integer elements of size at most $H$ and obtain upper and lower bounds on the number of distinct irreducible characteristic polynomials which correspond to these matrices
Externí odkaz:
http://arxiv.org/abs/2310.09052