caa a22 4500 467989508 CHVBK 20180323112541.0 cr unu---uuuuu 170328e19900301xx s 000 0 eng 10.1007/BF01571277 doi (NATIONALLICENCE)springer-10.1007/BF01571277 On the average number of direct factors of a finite Abelian group [Elektronische Daten] [Hartmut Menzer, René Seibold] Let $$T(x) = \sum\limits_{ord(G) \leqq x} {t(G),} $$ , wheret(G) define the number of direct factors of a finite Abelian group.E. Krätzel ([5]) defined a remainderΔ 1(x) in the asymptotic ofT(x) and proved $$\Delta _1 (x)<< x^{{5 \mathord{\left/ {\vphantom {5 {12}}} \right. \kern-\nulldelimiterspace} {12}}} \log ^4 x.$$ Using two different methods to estimate a special three-dimensional exponential sum we get the better results $$\Delta _1 (x)<< x^{{{282} \mathord{\left/ {\vphantom {{282} {683}}} \right. \kern-\nulldelimiterspace} {683}}} \log ^4 x$$ and $$\Delta _1 (x)<< x^{{{45} \mathord{\left/ {\vphantom {{45} {109}}} \right. \kern-\nulldelimiterspace} {109}} + \varepsilon } (\varepsilon > 0).$$ Springer-Verlag, 1990 Menzer Hartmut Sektion Mathematik, Universitätshochhaus FSU Jena, DDR-6900, JENA, German Democratic Republic aut Seibold René Sektion Mathematik, Universitätshochhaus FSU Jena, DDR-6900, JENA, German Democratic Republic aut Monatshefte für Mathematik Springer-Verlag 110/1(1990-03-01), 63-72 0026-9255 110:1<63 1990 110 605 https://doi.org/10.1007/BF01571277 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01571277 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Menzer Hartmut Sektion Mathematik, Universitätshochhaus FSU Jena, DDR-6900, JENA, German Democratic Republic aut NATIONALLICENCE 700 1- Seibold René Sektion Mathematik, Universitätshochhaus FSU Jena, DDR-6900, JENA, German Democratic Republic aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer-Verlag 110/1(1990-03-01), 63-72 0026-9255 110:1<63 1990 110 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer