On the asymptotics of the shifted sums of Hecke eigenvalue squares
On the asymptotics of the shifted sums of Hecke eigenvalue squares
Abstract The purpose of this paper is to obtain asymptotics of shifted sums of Hecke eigenvalue squares on average. We show that for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>X</m:mi> <m:mrow> <m:mfrac> <m:mn>2</m:mn> <m:mn>3</m:mn> </m:mfrac> <m:mo>+</m:mo> <m:mi>ϵ</m:mi> </m:mrow> </m:msup> <m:mo><</m:mo> <m:mi>H</m:mi> <m:mo><</m:mo> <m:msup> <m:mi>X</m:mi> <m:mrow> <m:mn>1</m:mn> <m:mo>-</m:mo> <m:mi>ϵ</m:mi> </m:mrow> </m:msup> </m:mrow> </m:math> …