Character sums over unions of intervals
Character sums over unions of intervals
Abstract Let q be a cube-free positive integer and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>χ</m:mi> <m:mspace width="3.33333pt" /> <m:mo>(</m:mo> <m:mtext>mod</m:mtext> <m:mspace width="3.33333pt" /> <m:mi>q</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> ${\chi ~(\text{mod}~q)}$ be a non-principal Dirichlet character. Our main result is a Burgess-type estimate for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mo>∑</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo>∈</m:mo> <m:mi>A</m:mi> </m:mrow> …