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<p>We obtain a formula for the <i>p</i>-adic valuation of weighted moments of central <i>L</i>-values of holomorphic cusp forms twisted by Dirichlet characters of order <i>p</i>. In some cases we give an arithmetic interpretation of the constants in the formula. The result is obtained via the study of the <i>digit map</i>, turning a horizontal <i>p</i>-adic measure into a vertical one, applied to the horizontal <i>p</i>-adic <i>L</i>-functions as defined by Kriz and Nordentoft (Horizontal<i> p</i>-adic L-functions, 2023).</p>

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p-adic moments of L-functions

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Daniel Kriz,
  • Asbjørn Christian Nordentoft

摘要

We obtain a formula for the p-adic valuation of weighted moments of central L-values of holomorphic cusp forms twisted by Dirichlet characters of order p. In some cases we give an arithmetic interpretation of the constants in the formula. The result is obtained via the study of the digit map, turning a horizontal p-adic measure into a vertical one, applied to the horizontal p-adic L-functions as defined by Kriz and Nordentoft (Horizontal p-adic L-functions, 2023).