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• W1979258889 abstract "In this paper we find a new lower bound on the number of imaginary quadratic extensions of the function field (mathbb{F}_{q}(x)) whose class groups have elements of a fixed odd order. More precisely, for q, a power of an odd prime, and g a fixed odd positive integer ≥ 3, we show that for every ε > 0, there are (gg q^{L(frac{1}{2}+frac{3}{2(g+1)}-epsilon)}) polynomials (f in mathbb{F}_{q}[x]) with (deg f=L), for which the class group of the quadratic extension (mathbb{F}_{q}(x, sqrt{f})) has an element of order g. This sharpens the previous lower bound (q^{L(frac{1}{2}+frac{1}{g})}) of Ram Murty. Our result is a function field analogue which is similar to a result of Soundararajan for number fields." @default.
• W1979258889 created "2016-06-24" @default.
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• W1979258889 date "2013-02-01" @default.
• W1979258889 modified "2023-09-24" @default.
• W1979258889 title "Divisibility of class numbers of imaginary quadratic function fields by a fixed odd number" @default.
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• W1979258889 doi "https://doi.org/10.1007/s12044-012-0105-4" @default.
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