caa a22 4500 445869143 CHVBK 20180317145506.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00605-009-0171-6 doi (NATIONALLICENCE)springer-10.1007/s00605-009-0171-6 The asymptotic formula in Waring's problem for one square and seventeen fifth powers [Elektronische Daten] [Jörg Brüdern, Koichi Kawada] Let R k,s(n) denote the number of solutions of the equation $${n= x^2 + y_1^k + y_2^k + \cdots + y_s^k}$$ in natural numbers x, y 1, . . . , y s. By a straightforward application of the circle method, an asymptotic formula for R k,s(n) is obtained when k ≥ 3 and s ≥ 2k-1+2. When k ≥ 6, work of Heath-Brown and Boklan is applied to establish the asymptotic formula under the milder constraint s ≥ 7 · 2k-4+3. Although the principal conclusions provided by Heath-Brown and Boklan are not available for smaller values of k, some of the underlying ideas are still applicable for k=5, and the main objective of this article is to establish an asymptotic formula for R 5,17(n) by this strategy. Springer-Verlag, 2009 Waring's problem nationallicence Asymptotic formula nationallicence Sums of one square and powers nationallicence Brüdern Jörg Institut für Algebra und Zahlentheorie, Universität Stuttgart, 70511, Stuttgart, Germany aut Kawada Koichi Department of Mathematics, Faculty of Education, Iwate University, 020-8550, Morioka, Japan aut Monatshefte für Mathematik Springer Vienna 162/4(2011-04-01), 385-407 0026-9255 162:4<385 2011 162 605 https://doi.org/10.1007/s00605-009-0171-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-009-0171-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brüdern Jörg Institut für Algebra und Zahlentheorie, Universität Stuttgart, 70511, Stuttgart, Germany aut NATIONALLICENCE 700 1- Kawada Koichi Department of Mathematics, Faculty of Education, Iwate University, 020-8550, Morioka, Japan aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 162/4(2011-04-01), 385-407 0026-9255 162:4<385 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer