Mean square value of exponential sums related to representation of integers as sum of two squares

Mean square value of exponential sums related to representation of integers as sum of two squares

1. Introduction. The problem we address here arises in the study of the error function in the shifted circle problem (see [BCDL]). Let α = (α 1 , α 2) ∈ R

Representing Integers as Sums of Squares

We study in detail the special case of Waring’s problem when the power k = 2. Ultimately, we prove that four is the least number of squares needed to represent any integer. To this end, we prove that some numbers cannot be represented as sums of two squares, some cannot be represented as sums of three, and all can be represented as sums of four. We also show that numbers of a certain form can b...

On the Hybrid Mean Value of Cochrane Sums and Two-term Exponential Sums

a synchronic and diachronic approach to the change route of address terms in the two recent centuries of persian language

terms of address as an important linguistics items provide valuable information about the interlocutors, their relationship and their circumstances. this study was done to investigate the change route of persian address terms in the two recent centuries including three historical periods of qajar, pahlavi and after the islamic revolution. data were extracted from a corpus consisting 24 novels w...

on direct sums of baer modules

the notion of baer modules was defined recently