{"title":"Discrete mean values of the product of derivatives of shifted Dirichlet L-functions","authors":"Hansle Cho","doi":"10.1016/j.jnt.2024.03.005","DOIUrl":null,"url":null,"abstract":"<div><p>Assuming the Generalized Riemann Hypothesis, we calculate <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mn>0</mn><mo><</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>χ</mi></mrow></msub><mo>≤</mo><mi>T</mi></mrow></msub><msup><mrow><mi>L</mi></mrow><mrow><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></msup><mo>(</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>χ</mi></mrow></msub><mo>+</mo><mi>i</mi><mi>δ</mi><mo>,</mo><mi>χ</mi><mo>)</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></msup><mo>(</mo><mn>1</mn><mo>−</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>χ</mi></mrow></msub><mo>−</mo><mi>i</mi><mi>δ</mi><mo>,</mo><mover><mrow><mi>χ</mi></mrow><mo>‾</mo></mover><mo>)</mo></math></span>, which extends the result proposed by Gonek in 1984.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24000787","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Assuming the Generalized Riemann Hypothesis, we calculate , which extends the result proposed by Gonek in 1984.
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