{"title":"A note on the exceptional set for sums of unlike powers of primes","authors":"Yuhui Liu","doi":"10.1007/s13226-024-00695-0","DOIUrl":null,"url":null,"abstract":"<p>In this paper, it is proved that with at most <span>\\(O(N^{\\frac{13}{96}+\\varepsilon })\\)</span> exceptions, every sufficiently large even integer satisfying <span>\\(n\\leqslant N\\)</span>, <span>\\(n\\not \\equiv 2\\,(\\textrm{mod}\\,3)\\)</span> can be represented as the sum of two squares of primes, one cube of primes and three biquadrates of primes. This result constitutes a refinement upon that of the author [6].</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00695-0","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
In this paper, it is proved that with at most \(O(N^{\frac{13}{96}+\varepsilon })\) exceptions, every sufficiently large even integer satisfying \(n\leqslant N\), \(n\not \equiv 2\,(\textrm{mod}\,3)\) can be represented as the sum of two squares of primes, one cube of primes and three biquadrates of primes. This result constitutes a refinement upon that of the author [6].
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