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On the exponent of the ideal class group of ๐‘„(โˆš-๐‘‘)

On the exponent of the ideal class group of ๐‘„(โˆš-๐‘‘)

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m left-parenthesis d right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">m(d)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the exponent of the ideal class group of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper Q left-parenthesis StartRoot negative d EndRoot right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow โ€ฆ