Scholarlink

<p>We study the distribution of the sequence of the first <i>N</i> elements of the discrete dynamical system generated by the Möbiustransformation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x \mapsto (\alpha x + \beta )/(\gamma x + \delta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>↦</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mi>x</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo stretchy="false">/</mo> <mo stretchy="false">(</mo> <mi>γ</mi> <mi>x</mi> <mo>+</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> over a finite field of <i>p</i> elements at the moments of time that correspond to <i>Q</i>-smooth numbers, that is, to numbers composed out of primes up to <i>Q</i>. In particular, we obtain nontrivial estimates of exponential sums with such sequences. This falls within the nowadays very active direction of investigating elements in orbits of dynamical systems at the moments of time of arithmetic interest.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the dynamical system generated by the möbius transformation at smooth times

  • 期刊论文

  • 发表日期：

    2025年11月6日

查看全文
  • László Mérai,
  • Igor E. Shparlinski

摘要

We study the distribution of the sequence of the first N elements of the discrete dynamical system generated by the Möbiustransformation \(x \mapsto (\alpha x + \beta )/(\gamma x + \delta )\) x ↦ ( α x + β ) / ( γ x + δ ) over a finite field of p elements at the moments of time that correspond to Q-smooth numbers, that is, to numbers composed out of primes up to Q. In particular, we obtain nontrivial estimates of exponential sums with such sequences. This falls within the nowadays very active direction of investigating elements in orbits of dynamical systems at the moments of time of arithmetic interest.