Mean values for a class of arithmetic functions in short intervals

Wu Jie; Wu Qiang

摘要

Abstract >In this paper, we shall establish a rather general asymptotic formula in short intervals for a class of arithmetic functions and announce two applications about the distribution of divisors of square‐full numbers and integers representable as sums of two?squares. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> 在本文中，我们将以短暂的间隔建立一个相当一般的渐近配方，用于一类算术函数，并宣布两种关于分配的平方数量分配的应用程序和表示的整数作为两个？平方的总和。</ P> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-24615/'>《Mathematische Nachrichten》</a> <b style="margin: 0 2px;">|</b><span>2020年第1期</span><b style="margin: 0 2px;">|</b><span>共25页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wu Jie&option=202" target="_blank" rel="nofollow">Wu Jie;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wu Qiang&option=202" target="_blank" rel="nofollow">Wu Qiang;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of MathematicsSouthwest University2 Tiansheng Road Beibei 400715 Chongqing China;</p> <p>Department of MathematicsSouthwest University2 Tiansheng Road Beibei 400715 Chongqing China;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/156.html" title="数学">数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=asymptotic results on arithmetic functions&option=203" rel="nofollow">asymptotic results on arithmetic functions;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=beta law&option=203" rel="nofollow">beta law;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Selberg–Delange method&option=203" rel="nofollow">Selberg–Delange method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=11N37&option=203" rel="nofollow">11N37;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=11N60&option=203" rel="nofollow">11N60;</a> </p> <div class="translation"> 机译：算术函数的渐近结果;β法;Selberg-delange方法;11n37;11n60; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704023596199.html">Mean values for a class of arithmetic functions in short intervals</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wu Jie&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Wu Jie,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wu Qiang&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Wu Qiang </a> <a href="/journal-foreign-24615/" target="_blank" rel="nofollow" class="tuijian_authcolor">Mathematische Nachrichten .</a> <span>2020</span><span>,第1期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：短期内一类算术函数的平均值</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704011718343.html">On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Bui H. 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