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Math."],"published-print":{"date-parts":[[2020,5,1]]},"abstract":"Abstract<\/jats:title>\n \n Let\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n be the set of positive integers whose binary decompositions contain an even number of ones. We give a bound for the trigonometric sum of special form over numbers in\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n ; using this bound, we derive an asymptotic formula for the number of solutions to Waring\u2019s equation in positive integers in\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n , and also a bound for the number of terms in the last equation, which is sufficient for the equation to be solvable in integers in\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n .\n <\/jats:p>\n Bibliography: 9 titles.<\/jats:p>","DOI":"10.1070\/sm9289","type":"journal-article","created":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T07:17:19Z","timestamp":1582010239000},"page":"733-749","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Waring\u2019s problem in natural numbers of special form"],"prefix":"10.4213","volume":"211","author":[{"given":"K. 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