On some products involving primes

Abstract

Asymptotic formulae are given for the products <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P Subscript l Baseline left-parenthesis x right-parenthesis left-parenthesis l equals 1 comma 3 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>l</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>l</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{P_l}(x)(l = 1,3)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> defined below.

Locations

• Proceedings of the American Mathematical Society - View - PDF