Primes from sums of two squares and missing digits

机译：从两个正方形和缺失的数字的总和的素质

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Abstract > Let <mat:math display="inline" altimg="urn:x-wiley:00246115:media:plms12307:plms12307-math-0001" wiley:location="equation/plms12307-math-0001.png"> <mat:msup> <mat:mi mathvariant="script">A</mat:mi> <mat:mo>′</mat:mo> </mat:msup> </mat:math> be the set of integers missing any three fixed digits from their decimal expansion. We produce primes in a thin sequence by proving an asymptotic formula for counting primes of the form <mat:math display="inline" altimg="urn:x-wiley:00246115:media:plms12307:plms12307-math-0002" wiley:location="equation/plms12307-math-0002.png"> <mat:mrow> <mat:mi>p</mat:mi> <mat:mo>=</mat:mo> <mat:msup> <mat:mi>m</mat:mi> <mat:mn>2</mat:mn> </mat:msup> <mat:mo>+</mat:mo> <mat:msup> <mat:mi>?</mat:mi> <mat:mn>2</mat:mn> </mat:msup> </mat:mrow> </mat:math> , with <mat:math display="inline" altimg="urn:x-wiley:00246115:media:plms12307:plms12307-math-0003" wiley:location="equation/plms12307-math-0003.png"> <mat:mrow> <mat:mi>?</mat:mi> <mat:mo>∈</mat:mo> <mat:msup> <mat:mi mathvariant="script">A</mat:mi> <mat:mo>′</mat:mo> </mat:msup> </mat:mrow> </mat:math> . > The proof draws on ideas from the work of Friedlander–Iwaniec on primes of the form <mat:math display="inline" altimg="urn:x-wiley:00246115:media:plms12307:plms12307-math-0004" wiley:location="equation/plms12307-math-0004.png"> <mat:mrow> <mat:mi>p</mat:mi> <mat:mo>=</mat:mo> <mat:msup> <mat:mi>x</mat:mi> <mat:mn>2</mat:mn> </mat:msup> <mat:mo>+</mat:mo> <mat:msup> <mat:mi>y</mat:mi> <mat:mn>4</mat:mn> </mat:msup> </mat:mrow> </mat:math> , as well as ideas from the work of Maynard on primes with restricted?digits. </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> > 让 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246115：Media：PLMS12307：PLMS12307-Math-0001”Wiley：Location =“等式/ PLMS12307-Math-0001.png”> <mat：msup> <mat：mi mathvariant =“script”> a </ mat：mi> <mat：mo>'</ mat：mo> </ mat：msup> </ mat：math> 是一组整数缺少从十进制扩展的任何三位固定数字。通过证明用于计数形式的次数的渐近公式，我们以薄序列产生稀有序列 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246115：Media：PLMS12307：PLMS12307-Math-0002”Wiley：Location =“等式/ PLMS12307-Math-0002.png”> <MAT：MROW> <MAT：MI> P </ MAT：MI> <mat：mo> = </ mat：mo> <mat：msup> <MAT：MI> M </ MAT：MI> <MAT：MN> 2 </ MAT：MN> </ mat：msup> <mat：mo> + </ mat：mo> <mat：msup> <mat：mi>？</ mat：mi> <MAT：MN> 2 </ MAT：MN> </ mat：msup> </ mat：MROW> </ mat：math> ，和 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246115：Media：PLMS12307：PLMS12307-Math-0003”Wiley：Location =“等式/ PLMS12307-Math-0003.png”> <MAT：MROW> <mat：mi>？</ mat：mi> <mat：mo>∈</ mat：mo> <mat：msup> <mat：mi mathvariant =“script”> a </ mat：mi> <mat：mo>'</ mat：mo> </ mat：msup> </ mat：MROW> </ mat：math> 。 </ p> > 证明在弗里德兰德 - 伊恩恩·伊恩恩·伊斯兰的思想上取决于表格的初步 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246115：Media：PLMS12307：PLMS12307-Math-0004”Wiley：Location =“等式/ PLMS12307-Math-0004.png”> <MAT：MROW> <MAT：MI> P </ MAT：MI> <mat：mo> = </ mat：mo> <mat：msup> <mat：mi> x </ mat：mi> <MAT：MN> 2 </ MAT：MN> </ mat：msup> <mat：mo> + </ mat：mo> <mat：msup> <MAT：MI> Y </ MAT：MI> <MAT：MN> 4 </ MAT：MN> </ mat：msup> </ mat：MROW> </ mat：math> 以及来自Maynard工作的想法在有限的近距离的素数。 </ 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-29812/'>《Proceedings of the London Mathematical Society》</a> <b style="margin: 0 2px;">|</b><span>2020年第6期</span><b style="margin: 0 2px;">|</b><span>共61页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> </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"> </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=11N05&option=203" rel="nofollow">11N05;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=11N32 (primary)&option=203" rel="nofollow">11N32 (primary);</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=11N36&option=203" rel="nofollow">11N36;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=11A63 (secondary)&option=203" rel="nofollow">11A63 (secondary);</a> </p> <div class="translation"> 机译：11n05;11n32（初级）;11n36;11a63（二次）; </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/0704024593312.html">Primes from sums of two squares and missing digits</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> </a> <a href="/journal-foreign-29812/" target="_blank" rel="nofollow" class="tuijian_authcolor">Proceedings of the London Mathematical Society .</a> <span>2020</span><span>,第6期</span> </span> </div> <p class="zwjiyix translation" style="max-width: 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class="enjiyixqcontent" href="/patent-detail/06130477532052.html">DEVICE FOR COMPUTING SQUARE ROOT OF TWO N-DIGIT NUMBER SQUARED SUM</a> <b>[P]</b> . <span> 外国专利：  SU877528A1 </span> <span> . 1981-10-30</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：计算两个N位数字平方和的平方根的设备 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130475164613.html">DEVICE FOR COMPUTING THE SUM OF SQUARES OF KN-DIGIT NUMBERS</a> <b>[P]</b> . <span> 外国专利：  SU993256A1 </span> <span> . 1983-01-30</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：计算KN-位数的平方和的设备 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130421821530.html">FUNCTIONAL STRUCTURE OF A TRANSFORMER OF PRELIMINARY FA f Σ n i amp;m i (2 n ) OF PARALLEL-SERIAL MULTIPLICATOR f Σ (Σ) CONDITIONALLY, OF "i" DIGIT TO SUM UP OF POSITIONAL ADDITIVE OF SUMS n i f(2 n ) AND m i f(2 n ) OF PARTIAL PRODUCTS USING ARITHMETICAL AXIOMS OF TERNARY NOTATION f(+1, 0, -1) WITH THE FORMATION OF A RESULTING SUM S Σ f(2 n ) IN A POSITIONAL FORMAT</a> <b>[P]</b> . <span> 外国专利：  RU2443008C1 </span> <span> . 2012-02-20</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：条件“ i”，“求和”求和累加和的“ i”数字的并行串乘乘法器fΣ[ni]＆[mi]（2 n）的初始变压器的功能结构使用三元表示法f（+1，0，-1）的算术公理，在A的结果总和[SΣ] f（2 n）的形式下，生成部分产品的（2 n）和[mi] f（2 n）位置格式 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" 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