Computational intractability of attractors in the real quadratic family
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DOI: 10.1016/j.aim.2019.04.033
Abstract: We show that there exist real quadratic maps of the interval whose attractors are computationally intractable. This is the first known class of such natural examples. read more here.
Keywords: intractability attractors; quadratic family; computational intractability; attractors real ... See more keywords
Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group
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DOI: 10.1016/j.jnt.2016.09.030
Abstract: Abstract Let k be a real quadratic number field with 2-class group C 2 ( k ) isomorphic to Z / 2 m Z x Z / 2 n Z , m ≥ 1 ,… read more here.
Keywords: class; field; class group; number ... See more keywords
Corrigendum to “Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group” [J. Number Theory 173 (2017) 529–546]
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DOI: 10.1016/j.jnt.2017.03.023
Abstract: Abstract This corrigendum describes a number of calculation and typographical errors, primarily in the examples, in the 2017 JNT paper Some Real Quadratic Number Fields with their Hilbert 2-Class Field Having Cyclic 2-Class Group, by… read more here.
Keywords: fields hilbert; class; number fields; number ... See more keywords
On the theory of normalized Shintani L-functions and its application to Hecke L-functions, I: Real quadratic fields
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DOI: 10.1016/j.jnt.2018.11.023
Abstract: Abstract We define the class of normalized Shintani L-functions of several variables. Unlike Shintani zeta functions, the normalized Shintani L-function is a holomorphic function. Moreover it satisfies a good functional equation. We show that Hecke… read more here.
Keywords: theory normalized; real quadratic; normalized shintani; shintani functions ... See more keywords
Distribution of Class Numbers in Continued Fraction Families of Real Quadratic Fields
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DOI: 10.1017/s0013091518000159
Abstract: Abstract We construct a random model to study the distribution of class numbers in special families of real quadratic fields ${\open Q}(\sqrt d )$ arising from continued fractions. These families are obtained by considering continued… read more here.
Keywords: quadratic fields; class numbers; real quadratic; distribution class ... See more keywords
HEURISTICS FOR $p$ -CLASS TOWERS OF REAL QUADRATIC FIELDS
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DOI: 10.1017/s1474748019000641
Abstract: Abstract Let $p$ be an odd prime. For a number field $K$ , we let $K_{\infty }$ be the maximal unramified pro- $p$ extension of $K$ ; we call the group $\text{Gal}(K_{\infty }/K)$ the $p$… read more here.
Keywords: field; class tower; real quadratic; tower group ... See more keywords
Singular moduli for real quadratic fields: A rigid analytic approach
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DOI: 10.1215/00127094-2020-0035
Abstract: A rigid meromorphic cocycle is a class in the rst cohomology of the discrete group Γ := SL2(Z[1/p]) with values in the multiplicative group of non-zero rigid meromorphic functions on the p-adic upper half plane… read more here.
Keywords: moduli real; singular moduli; rigid meromorphic; fields rigid ... See more keywords