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pro vyhledávání: '"11N25, 11N32"'
Autor:
Zarhin, Yuri G.
This is an exposition of results of R.C. Vaughan and the author (Mathematika 70 (2024), no. 4). We discuss how often the squarefree values of an integral polynomial do occur. We discuss interrelations between our results and results of B. Poonen (arX
Externí odkaz:
http://arxiv.org/abs/2410.09357
Autor:
Pascadi, Alexandru
We prove new large sieve inequalities for the Fourier coefficients $\rho_{j\mathfrak{a}}(n)$ of exceptional Maass forms of a given level, weighted by sequences $(a_n)$ with sparse Fourier transforms - including two key types of sequences that arise i
Externí odkaz:
http://arxiv.org/abs/2404.04239
Autor:
Mounier, Adrien
Let $\mathcal{A}$ be a finite set of positive integers and $y\geq 1$. We give an effective lower bound of the cardinality of the set $\{n\in\mathcal{A};\,p|n\Longrightarrow p\leq y\}$ under the condition of a good knowledge of the level of distributi
Externí odkaz:
http://arxiv.org/abs/2402.13198
Autor:
Kalmynin, Alexander, Konyagin, Sergei
For a polynomial $f(x)\in \mathbb Z[x]$ we study an analogue of Jacobsthal function, defined by the formula \[ j_f(N)=\max_{m}\{\text{For some } x\in \mathbb N \text{ the inequality } (x+f(i),N)>1 \text{ holds for all }i\leq m\}. \] We prove a lower
Externí odkaz:
http://arxiv.org/abs/2302.00459
Autor:
Goudout, Élie
Publikováno v:
J. Th\'eor. Nombres Bordeaux, 31(2)(2019):385-402
We study the simultaneous concentration of the values of several additive functions along polynomial shifts. Under a slight restriction, this yields an extension of a result from Hal\'asz in 1975.
Comment: 18 pages, in French
Comment: 18 pages, in French
Externí odkaz:
http://arxiv.org/abs/1809.06599
Autor:
Tenenbaum, Gérald
Let $\alpha\in]0,1]$ and let $Q_j$ $(1\leqslant j\leqslant r)$ denote distinct irreducible polynomials with integer coefficients. We show that, for vectors with coordinates not exceeding a constant multiple of their mean, the joint local distribution
Externí odkaz:
http://arxiv.org/abs/1710.04877
Autor:
Carella, N. A.
A recent heuristic argument based on basic concepts in spectral analysis showed that the twin prime conjecture and a few other related primes counting problems are valid. A rigorous version of the spectral method, and a proof of the more general dePo
Externí odkaz:
http://arxiv.org/abs/1509.00457
Autor:
Gérald Tenenbaum
Publikováno v:
Journal of Number Theory
Journal of Number Theory, Elsevier, 2018, 188, pp.88-95. ⟨10.1016/j.jnt.2018.01.005⟩
Journal of Number Theory, Elsevier, 2018, 188, pp.88-95. ⟨10.1016/j.jnt.2018.01.005⟩
Let $\alpha\in]0,1]$ and let $Q_j$ $(1\leqslant j\leqslant r)$ denote distinct irreducible polynomials with integer coefficients. We show that, for vectors with coordinates not exceeding a constant multiple of their mean, the joint local distribution
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e488ae2b5a05c3d3b7c2e78f524f0a5
https://hal.archives-ouvertes.fr/hal-02890615
https://hal.archives-ouvertes.fr/hal-02890615
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