Abstract:We apply Tatuzawa's version of Siegel's theorem to derive two lower bounds on the size of the principal genus of positive definite binary quadratic forms.
“…This is unconditional. However, a little arithmetic show that the interval ( 7) is nonempty only when (9) h(−D) < D 1/2 log(D) 74 .…”
Section: Expositionmentioning
confidence: 99%
“…From Lemma 2 of [9] we have that where W(x) denotes the Lambert W-function, i.e. the inverse function of f (w) = w exp(w) (see [3], [13, p. 146 and p. 348, ex 209]).…”
“…This is unconditional. However, a little arithmetic show that the interval ( 7) is nonempty only when (9) h(−D) < D 1/2 log(D) 74 .…”
Section: Expositionmentioning
confidence: 99%
“…From Lemma 2 of [9] we have that where W(x) denotes the Lambert W-function, i.e. the inverse function of f (w) = w exp(w) (see [3], [13, p. 146 and p. 348, ex 209]).…”
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