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Creators/Authors contains: "Thamminana, Aman_Dhruva"

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  1. ; ; (, The Ramanujan Journal)
    Abstract We prove that there are$$\gg \frac{X^{\frac{1}{3}}}{(\log X)^2}$$ ≫ X 1 3 ( log X ) 2 imaginary quadratic fieldskwith discriminant$$|d_k|\le X$$ | d k | ≤ X and an ideal class group of 5-rank at least 2. This improves a result of Byeon, who proved the lower bound$$\gg X^{\frac{1}{4}}$$ ≫ X 1 4 in the same setting. We use a method of Howe, Leprévost, and Poonen to construct a genus 2 curveCover$$\mathbb {Q}$$ Q such thatChas a rational Weierstrass point and the Jacobian ofChas a rational torsion subgroup of 5-rank 2. We deduce the main result from the existence of the curveCand a quantitative result of Kulkarni and the second author. 
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