短区间内一素数幂与四素数立方的和

IF 0.7 Q2 MATHEMATICS Muenster Journal of Mathematics Pub Date : 2023-06-01 DOI:10.1155/2023/3244257

Gen Li, Xianjiu Huang, Xiaoming Pan, Li Yang

{"title":"短区间内一素数幂与四素数立方的和","authors":"Gen Li, Xianjiu Huang, Xiaoming Pan, Li Yang","doi":"10.1155/2023/3244257","DOIUrl":null,"url":null,"abstract":"Let \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mi>k</mi>\n <mo>⩾</mo>\n <mn>1</mn>\n </math>\n be an integer. In this study, we derive an asymptotic formula for the average number of representations of integers \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>n</mi>\n <mo>=</mo>\n <msubsup>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n <mrow>\n <mi>k</mi>\n </mrow>\n </msubsup>\n <mo>+</mo>\n <msubsup>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msubsup>\n <mo>+</mo>\n <msubsup>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msubsup>\n <mo>+</mo>\n <msubsup>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>4</mn>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msubsup>\n <mo>+</mo>\n <msubsup>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>5</mn>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msubsup>\n </math>\n in short intervals, where \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <msub>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>4</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mi>p</mi>\n </mrow>\n <mrow>\n <mn>5</mn>\n </mrow>\n </msub>\n </math>\n are prime numbers.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sums of One Prime Power and Four Prime Cubes in Short Intervals\",\"authors\":\"Gen Li, Xianjiu Huang, Xiaoming Pan, Li Yang\",\"doi\":\"10.1155/2023/3244257\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let \\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <mi>k</mi>\\n <mo>⩾</mo>\\n <mn>1</mn>\\n </math>\\n be an integer. In this study, we derive an asymptotic formula for the average number of representations of integers \\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <mi>n</mi>\\n <mo>=</mo>\\n <msubsup>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n <mrow>\\n <mi>k</mi>\\n </mrow>\\n </msubsup>\\n <mo>+</mo>\\n <msubsup>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>2</mn>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msubsup>\\n <mo>+</mo>\\n <msubsup>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msubsup>\\n <mo>+</mo>\\n <msubsup>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>4</mn>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msubsup>\\n <mo>+</mo>\\n <msubsup>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>5</mn>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msubsup>\\n </math>\\n in short intervals, where \\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <msub>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>2</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>4</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n <mrow>\\n <mn>5</mn>\\n </mrow>\\n </msub>\\n </math>\\n are prime numbers.\",\"PeriodicalId\":43667,\"journal\":{\"name\":\"Muenster Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Muenster Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2023/3244257\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Muenster Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2023/3244257","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}