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<p>We extend known methods to establish upper bounds on the least character non-residues contingent on different zero-free regions within the critical strip, in particular on bounded rectangles within the critical strip along the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma =1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>σ</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> line at arbitrary heights. This relates to earlier conditional results on least character non-residues, and recent results of Granville and Soundararajan, on character sums.</p>

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Conditional upper bounds on the least character non-residue

  • 期刊论文

  • 发表日期：

    2026年5月16日

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  • Aritro Pathak

摘要

We extend known methods to establish upper bounds on the least character non-residues contingent on different zero-free regions within the critical strip, in particular on bounded rectangles within the critical strip along the \(\sigma =1\) σ = 1 line at arbitrary heights. This relates to earlier conditional results on least character non-residues, and recent results of Granville and Soundararajan, on character sums.