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• W2892373835 abstract "In this note we revisit classic work of Soundararajan on class groups of imaginary quadratic fields. Let $A,B,g ge 3$ be positive integers such that $gcd(A,B)$ is square-free. We refine Soundararajan's result to show that if $4 nmid g$ or if $A$ and $B$ satisfy certain conditions, then the number of negative square-free $D equiv A pmod{B}$ down to $-X$ such that the ideal class group of $mathbb{Q} (sqrt{D})$ contains an element of order $g$ is bounded below by $X^{frac{1}{2} + epsilon(g) - epsilon}$, where the exponent is the same as in Soundararajan's theorem. Combining this with a theorem of Frey, we give a lower bound for the number of quadratic twists of certain elliptic curves with $p$-Selmer group of rank at least $2$, where $p in {3,5,7}$." @default.
• W2892373835 created "2018-09-27" @default.
• W2892373835 creator A5046893825 @default.
• W2892373835 date "2018-09-15" @default.
• W2892373835 modified "2023-09-27" @default.
• W2892373835 title "Class number divisibility for imaginary quadratic fields" @default.
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• W2892373835 hasPublicationYear "2018" @default.
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