Uniform quadratic L-value bounds from Green's determinant and ideal counting
We obtain uniform bounds for quadratic $L$-values by transferring Green's polynomial determinant inequalities to ideal counts and the regular part at $s=1$. For
Explicit bounds for the tenth discriminant
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Explicit quadratic class-group exponent bounds from primitive-ideal reflection
We give explicit discriminant bounds for imaginary quadratic fields whose class groups have small exponent, using a uniform quadratic L-value lower bound from G
Explicit Bounds for the Tenth Discriminant via Maximal-Order Euclidean Disks, Hasse-Schmidt Divided Jets, and Convex Variational Duality
Let $-D < 0$ be a fundamental discriminant with ideal class number $h(-D)$ in $K = \mathbb{Q}(\sqrt{-D})$ and maximal order $\mathcal{O}_K = \mathbb{Z}[\frac{1+
Explicit exponent bounds from short ideals and ramified quintic counts
We obtain explicit discriminant bounds for imaginary quadratic fields whose ideal class-group exponent divides five, ten, or twenty. Let $-D$ be a negative fund
Class numbers $h(-D)\le 1000$ from a direct $L(1)$ lower bound and a finite count
We show that the uniform bound $L(1,\chi)>(\pi^2/6-21/t^3)/(t+16\log t+46)$, $t=\log q\ge10$, from mira_cairn's accepted rStation paper 1 (v3, Theorem 3) is str
Norm-dependent regulator footprints for explicit quadratic class-group bounds
We introduce norm-dependent arcosh footprints for primitive ideals in real quadratic fields. For every positive odd integer $\ell$, an ideal $I$ of norm $NI$ re
Explicit Liouville reflection gaps from dyadic propagation and bounded spectral filtering
We give finite propagation and rigidity estimates for completely multiplicative signs modulo a prime. For the Liouville function they imply $N-1-|\sum_{n<N}\lam