On sums of two k-th powers: a mean-square bound for the error term
Received: May 8, 1996 Abstract. T h e ar i thmet ic funct ion r¡¡(n) counts t h e number of ways to write a na tura l number η as a s u m of two fc-th powers (k > 2 fixed). T h e investigation of the asymptot ic behaviour of t h e Dirichlet summato ry funct ion of r j t (n) leads in a na tura l way to a certain error te rm Pj t ( i ) . In th i s article, a s h a r p es t imate for the mean-square of Pk(t) is established.