Ramanujan’s function <i>k</i>(<i>τ</i>)=<i>r</i>(<i>τ</i>)<i>r</i> <sup>2</sup>(2<i>τ</i>) and its modularity
Ramanujan’s function <i>k</i>(<i>τ</i>)=<i>r</i>(<i>τ</i>)<i>r</i> <sup>2</sup>(2<i>τ</i>) and its modularity
Abstract We study the modularity of Ramanujan’s function <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> <m:mo stretchy="false">(</m:mo> <m:mi>τ</m:mi> <m:mo stretchy="false">)</m:mo> <m:mo>=</m:mo> <m:mi>r</m:mi> <m:mo stretchy="false">(</m:mo> <m:mi>τ</m:mi> <m:mo stretchy="false">)</m:mo> <m:msup> <m:mrow> <m:mi>r</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msup> <m:mo stretchy="false">(</m:mo> <m:mn>2</m:mn> <m:mi>τ</m:mi> <m:mo stretchy="false">)</m:mo> </m:math> k(\tau )=r(\tau ){r}^{2}(2\tau ) , where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>r</m:mi> <m:mo stretchy="false">(</m:mo> <m:mi>τ</m:mi> <m:mo stretchy="false">)</m:mo> …