Type: Article
Publication Date: 1974-01-01
Citations: 14
DOI: https://doi.org/10.1090/s0025-5718-1974-0352042-5
This paper covers many (closely related) topics: the distribution of the 3-Sylow subgroups of imaginary quadratic fields; the possibility of finding 3-ranks greater than 4; some questions concerning <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a cubed equals b squared plus c squared upper D"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>a</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:mo>+</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{a^3} = {b^2} + {c^2}D</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; and the convergence of Euler products and its relation to the extended Riemann hypothesis. Two programs that were used in this investigation are described.