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<p>In this article, we study the distribution of the irrational factor function of order <i>k</i>. We introduce the irrational factor function in both number field and function field settings, derive asymptotic formulas for their average value, and further establish omega results for the error term in the asymptotic formulas. Moreover, we study the Chebyshev’s bias phenomenon for number field and function field analogues of sum of the irrational factor function, under assumptions on the real zeros of Hecke <i>L</i>-functions associated with Hecke characters in the number field case.</p>

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Chebyshev’s bias for irrational factor function

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Bittu Chahal

摘要

In this article, we study the distribution of the irrational factor function of order k. We introduce the irrational factor function in both number field and function field settings, derive asymptotic formulas for their average value, and further establish omega results for the error term in the asymptotic formulas. Moreover, we study the Chebyshev’s bias phenomenon for number field and function field analogues of sum of the irrational factor function, under assumptions on the real zeros of Hecke L-functions associated with Hecke characters in the number field case.