On exponential sums involving the divisor function over Z[๐]
Journal Title: ะะพัะปัะดะถะตะฝะฝั ะฒ ะผะฐัะตะผะฐัะธัั ั ะผะตั ะฐะฝััั - Year 2016, Vol 21, Issue 2
Abstract
We apply the van der Corput transform to investigate the sums of view ฮฃ๏ธ ๐(๐)๐(๐)๐(๐(๐))), where ๐(๐) is the number of representations of ๐ as the sum of two squares of integer numbers. Such sums have been studied by M. Jutila, O. Gunyavy, M. Huxley and etc. Depending of differential properties of the functions ๐(๐) and ๐(๐) there have been obtained the different kinds of error terms in bounds of the considered sums. In the special case, O. Gunyavy improved the result of M. Jutila in the problem on estimate the exponential sum involving the divisor function ๐ (๐). We obtain the asymptotic formula of the sum ฮฃ๏ธ ๐ (๐ผ)๐ (๏ธ ๐ ๐๐(๐ผ) )๏ธ over the ring of Gaussian integers which is an analogue of the asymptotic formulas obtained by M. Jutila and O. Gunyavy. MSC: 11K45.
Authors and Affiliations
S. Varbanets
Keywords
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