On Montgomery’s pair correlation conjecture: A tale of three integrals
On Montgomery’s pair correlation conjecture: A tale of three integrals
Abstract We study three integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. The first is the integral of Montgomery’s function <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>F</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>T</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {F(\alpha,T)} in bounded intervals, the second is an integral introduced …