Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc31852/eng.pdf Дата изменения: Mon Oct 1 22:02:38 2012 Дата индексирования: Mon Oct 1 22:02:38 2012 Кодировка:

ON THE ESTIMATION OF EXPONENTIAL SUMS DEALT WITH LATTICE POINTS DISTRIBUTION IN THREE-DIMENSIONAL AREAS Arkhipova L.G. The Moscow state university of .V. Lomonosov, fac. of mathematics and mechanics, sec. of Mathematical analysis, Russia, 119992, Moscow, Lenin hills 1. phone: (495) 939-18-01 When we estimate error terms in the sphere problem and in problem of averages of class number of imaginary quadrate fields, we should be interested in estimation of exponential sums S like this S=
v k ,m ,n , 2 v



e

2 i a k 2 + m 2 + n

2

,

where a + , v < < a 2 3 . The best previous estimation of such sums was made by Vinogradov I.M. in [1]. The estimation is S < < a 3 + . This inequality gives us the opportunity to estimate the error term R(a) in the sphere problem as R (a ) < < a 3 + . We give the method that allows us to obtain the estimation 5 1 - + , where = . S < < a3 45 This implies new error term R(a) estimation in the sphere problem of the type R(a ) < < a
59 + 45 4 5

.

References. 1. .. . - .: , 1976, 33.