We suspect that the “genus part” of the class number of a number field K may be an
obstruction for an “easy and unconditional proof” of the classical p-rank ε-conjecture for p …

This paper is a continuation of [2]. We construct unconditionally several families of number
fields with large class numbers. They are number fields whose Galois closures have as the …

Explicit estimates for Artin L-functions: Duke's short-sum theorem and Dedekind zeta residues -
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Let T be an algebraic torus over ℚ such that T (ℝ) is compact. Assuming the generalized
Riemann hypothesis, we give a lower bound for the size of the class group of T modulo its n …

arXiv:2101.11853v3 [math.NT] 18 Feb 2021 Page 1 EXPLICIT ESTIMATES FOR ARTIN L-FUNCTIONS:
DUKE’S SHORT-SUM THEOREM AND APPLICATIONS STEPHAN RAMON GARCIA AND …

Let p $\ge $2 be a given prime number. We prove, for any number field kappa and any
integer e $\ge $1, the p-rank $\epsilon $-conjecture, on the p-class groups Cl\_F, for the …

Some PARI programs have bringed out a property for the non-genus part of the class
number of the imaginary quadratic fields, with respect to $(\sqrt D\,)^{\varepsilon} $, where …

Some PARI/GP programs have shown a new interesting regularity phenomenon for the
order h of the non-genus part of the class group of imaginary quadratic fields, with respect to …

In this thesis we study the André-Oort conjecture, which is a statement regarding
subvarieties of Shimura varieties that contain a Zariski dense set of special points. In …