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Heuristics on class groups of number fields
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/bf01199694openalex-snapshot
A partition formula connected with Abelian groups
inferredcites →https://doi.org/10.1007/bfb0061302openalex-snapshot
The Selberg Trace Formula for PSL(2,ℝ)
inferredcites →https://doi.org/10.1007/bfb0079608openalex-snapshot
The Selberg Trace Formula for PSL(2,ℝ) Volume I
inferredcites →https://doi.org/10.1017/cbo9780511662027.007openalex-snapshot
On the calculation of regulators and class numbers of quadratic fields
inferredcites →https://doi.org/10.1090/s0025-5718-1976-0404205-xopenalex-snapshot
Class Groups of Quadratic Fields
inferredcites →https://doi.org/10.1098/rspa.1971.0075openalex-snapshot
On the density of discriminants of cubic fields. II
inferredcites →https://doi.org/10.1515/crll.1975.277.89openalex-snapshot
Méthodes et algorithmes pour le calcul numérique du nombre de classes et de unités des extensions cubiques cycliques de Q.
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Cyclicity Statistics for Elliptic Curves over Finite Fields
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Gauss Problem for Function Fields
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Exponents of Class Groups and Elliptic Curves
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Cohen–Lenstra Heuristics and the Spiegelungssatz: Number Fields
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A Note on the Divisibility of Class Numbers of Real Quadratic Fields
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Algorithmic Methods for Finitely Generated Abelian Groups
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Intractable Problems in Number Theory
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A key exchange system based on real quadratic fields Extended abstract
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Cohen–Lenstra Heuristics of Quadratic Number Fields
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Numerical Results on Class Groups of Imaginary Quadratic Fields
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The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography
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Security of Cryptosystems Based on Class Groups of Imaginary Quadratic Orders
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Towards Practical Non-interactive Public Key Cryptosystems Using Non-maximal Imaginary Quadratic Orders (Extended Abstract)
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Algorithms for Large Integer Matrix Problems
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Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups
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First Implementation of Cryptographic Protocols Based on Algebraic Number Fields
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p-adic Galois Representations and pro-p Galois Groups
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Improved Efficiency of a Linearly Homomorphic Cryptosystem
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Quantum Security Analysis of CSIDH
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Further Optimizations of CSIDH: A Systematic Approach to Efficient Strategies, Permutations, and Bound Vectors
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Secure Multiparty Computation from Threshold Encryption Based on Class Groups
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Short Representation of Quadratic Integers
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Efficient Post-quantum Commutative Group Actions from Orientations of Large Discriminant
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A Collage of Results on the Divisibility and Indivisibility of Class Numbers of Quadratic Fields
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Parameterized Families of Quadratic Fields with n-Rank at Least 2
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Key-exchange in real quadratic congruence function fields
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The 4-class ranks of quadratic fields
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Trace formulae and imaginary quadratic fields
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A key-exchange system based on imaginary quadratic fields
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Modification of Cohen-Lenstra heuristics for ideal class groups and numbers of certain real quadratic fields
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Tate and Ate pairings fory 2 =x 5 − αx in characteristic five
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Experimental results on class groups of real quadratic fields
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Half-factorial real quadratic orders
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Counterexamples to a conjecture of Lemmermeyer
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Some Finite Abelian Group Theory and Some $${q}$$ q -Series Identities
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Non-vanishing of Geodesic Periods of Automorphic Forms
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Arakelov class groups of random number fields
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Publisher Correction to: Finite quotients of 3-manifold groups
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Real quadratic fields with class number divisible by 3
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Real Quadratic Fields with Class Number Divisible by 5 or 7
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Imaginary quadratic fields with class groups of 3-rank at least 2
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Topology and Geometry of Random 2-Dimensional Hypertrees
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A Note on the Distribution of Iwasawa Invariants of Imaginary Quadratic Fields
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Relative ideal classes of arbitrary order
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On large Iwasawa $$\uplambda $$-invariants of imaginary quadratic function fields
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The divisibility of the class number of the imaginary quadratic fields $${\mathbb {Q}}(\sqrt{1-2m^k})$$
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The 2-torsion of determinantal hypertrees is not Cohen–Lenstra
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Divisibility of class numbers of imaginary quadratic function fields by a fixed odd number
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Problems in arithmetic topology
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Harmonic analysis and statistics of the first Galois cohomology group
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Corrigendum to “Harmonic analysis and statistics of the first Galois cohomology group”
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The first level of $$\mathbb Z_p$$-extensions and compatibility of heuristics
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The weak form of Malle’s conjecture and solvable groups
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Class number divisibility for imaginary quadratic fields
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Field change for the Cassels–Tate pairing and applications to class groups
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Fast square-free decomposition of integers using class groups
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Class groups of imaginary biquadratic fields
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The 4-class ranks of quadratic extensions of certain real quadratic fields
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Sandpile groups and the coeulerian property for random directed graphs
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A weighted Möbius function
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The Cohen–Lenstra heuristic: Methodology and results
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Abelian subgroups of any order in class groups of global function fields
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A combinatorial interpretation of the probabilities of p-groups in the Cohen–Lenstra measure
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Cohen–Lenstra heuristic and roots of unity
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Class number indivisibility for quadratic function fields
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Visibility of ideal classes
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A class group heuristic based on the distribution of 1-eigenspaces in matrix groups
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Class numbers in cyclotomic Zp -extensions
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Valuations of p-adic regulators of cyclic cubic fields
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Indivisibility of relative class numbers of totally imaginary quadratic extensions and vanishing of these relative Iwasawa invariants
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Genus theory and ε-conjectures on p-class groups
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Invariant part of class groups and distribution of relative class group
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The distribution of class groups of function fields
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An Introduction to Probabilistic Number Theory
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Exponents of the class groups of imaginary Abelian number fields
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SIMULTANEOUS BOUNDING OF 4 $4$ 4 -RANKS IN NARROW CLASS GROUPS OF QUADRATIC FIELDS
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ON MODpREPRESENTATIONS WHICH ARE DEFINED OVERp: II
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Prime decomposition and the Iwasawa MU-invariant
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The cokernel of a polynomial push-forward of a random integral matrix with concentrated residue
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Abelian groups from random hypergraphs
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CLASSIFICATION AND SYMMETRIES OF A FAMILY OF CONTINUED FRACTIONS WITH BOUNDED PERIOD LENGTH
inferred← citeshttps://doi.org/10.1017/s1446788724000156openalex-snapshot
CLASS GROUP STATISTICS FOR TORSION FIELDS GENERATED BY ELLIPTIC CURVES
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Random Dieudonné modules, random -divisible groups, and random curves over finite fields
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THE DISTRIBUTION OF TORSION SUBSCHEMES OF ABELIAN VARIETIES
inferred← citeshttps://doi.org/10.1017/s1474748019000641openalex-snapshot
HEURISTICS FOR -CLASS TOWERS OF REAL QUADRATIC FIELDS
inferred← citeshttps://doi.org/10.1017/s1474748020000651openalex-snapshot
ON THE -RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS
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The average size of 3-torsion in class groups of 2-extensions
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On the Mean 3-Rank of Quadratic Fields
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Indivisibility of Class Numbers of Real Quadratic Fields
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Cryptography in Quadratic Function Fields
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A Signature Scheme Based on the Intractability of Computing Roots
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Higher-rank zeta functions for elliptic curves
inferred← citeshttps://doi.org/10.1073/pnas.2005984117openalex-snapshot
Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers
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A Quick Route to Unique Factorization in Quadratic Orders
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The Number of Real Quadratic Fields Having Units of Negative Norm
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An Investigation of Bounds for the Regulator of Quadratic Fields
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The Size of the Fundamental Solutions of Consecutive Pell Equations
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Heuristics on Tate-Shafarevitch Groups of Elliptic Curves Defined over Q
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Computing the Modular Degree of an Elliptic Curve
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New Computations Concerning the Cohen-Lenstra Heuristics
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A Note on Jacobians, Tutte Polynomials, and Two-Variable Zeta Functions of Graphs
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Missing Class Groups and Class Number Statistics for Imaginary Quadratic Fields
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Cohen–Lenstra Heuristics for Torsion in Homology of Random Complexes
inferred← citeshttps://doi.org/10.1080/10586458.2021.2011492openalex-snapshot
Heuristics for 2-class Towers of Cyclic Cubic Fields
inferred← citeshttps://doi.org/10.1090/amsip/007/03openalex-snapshot
Elliptic and modular curves over finite fields and related computational issues
inferred← citeshttps://doi.org/10.1090/btran/140openalex-snapshot
On Malle’s conjecture for nilpotent groups
inferred← citeshttps://doi.org/10.1090/btran/90openalex-snapshot
On unit signatures and narrow class groups of odd degree abelian number fields
inferred← citeshttps://doi.org/10.1090/cbms/102/08openalex-snapshot
Class numbers of quadratic fields
inferred← citeshttps://doi.org/10.1090/conm/701/14145openalex-snapshot
A refinement of a conjecture of Gross, Kohnen, and Zagier
inferred← citeshttps://doi.org/10.1090/conm/796/15995openalex-snapshot
Improved methods for finding imaginary quadratic fields with high 𝑛-rank
inferred← citeshttps://doi.org/10.1090/conm/796/15996openalex-snapshot
Unconditional computation of the class groups of real quadratic fields
inferred← citeshttps://doi.org/10.1090/conm/818/16374openalex-snapshot
Counting matrix points on certain varieties over finite fields
inferred← citeshttps://doi.org/10.1090/fic/041/12openalex-snapshot
Heuristics for class numbers of prime-power real cyclotomic fields
inferred← citeshttps://doi.org/10.1090/jams/1062openalex-snapshot
The distribution of ℓ^{∞}-Selmer groups in degree ℓ twist families I
inferred← citeshttps://doi.org/10.1090/jams/866openalex-snapshot
The distribution of sandpile groups of random graphs
inferred← citeshttps://doi.org/10.1090/mcom/3395openalex-snapshot
Heuristics in direction of a p-adic Brauer--Siegel theorem
inferred← citeshttps://doi.org/10.1090/proc/13058openalex-snapshot
Small height in fields generated by singular moduli
inferred← citeshttps://doi.org/10.1090/proc/16543openalex-snapshot
Cotorsion of anti-cyclotomic Selmer groups on average
inferred← citeshttps://doi.org/10.1090/s0002-9939-02-06603-0openalex-snapshot
On the number of real quadratic fields with class number divisible by 3
inferred← citeshttps://doi.org/10.1090/s0002-9939-06-08291-8openalex-snapshot
Regularized product expressions of higher Riemann zeta functions
inferred← citeshttps://doi.org/10.1090/s0002-9939-06-08396-1openalex-snapshot
Counting abelian group structures
inferred← citeshttps://doi.org/10.1090/s0002-9939-1987-0866419-3openalex-snapshot
Densities for ranks of certain parts of 𝑝-class groups
inferred← citeshttps://doi.org/10.1090/s0025-5718-02-01432-1openalex-snapshot
Class numbers of real cyclotomic fields of prime conductor
inferred← citeshttps://doi.org/10.1090/s0025-5718-04-01632-1openalex-snapshot
On quadratic fields with large 3-rank
inferred← citeshttps://doi.org/10.1090/s0025-5718-04-01725-9openalex-snapshot
𝑝-class groups of certain extensions of degree 𝑝
inferred← citeshttps://doi.org/10.1090/s0025-5718-06-01850-3openalex-snapshot
Quadratic class numbers and character sums
inferred← citeshttps://doi.org/10.1090/s0025-5718-06-01890-4openalex-snapshot
Implementing the asymptotically fast version of the elliptic curve primality proving algorithm
inferred← citeshttps://doi.org/10.1090/s0025-5718-06-01921-1openalex-snapshot
Heuristics for class numbers and lambda invariants
inferred← citeshttps://doi.org/10.1090/s0025-5718-07-02001-7openalex-snapshot
Construction of hyperelliptic function fields of high three-rank
inferred← citeshttps://doi.org/10.1090/s0025-5718-08-02169-8openalex-snapshot
On the computation of class numbers of real abelian fields
inferred← citeshttps://doi.org/10.1090/s0025-5718-1986-0856717-9openalex-snapshot
Some Remarks on Cohen-Lenstra Heuristics
inferred← citeshttps://doi.org/10.1090/s0025-5718-1987-0866100-9openalex-snapshot
Class Groups of Quadratic Fields. II
inferred← citeshttps://doi.org/10.1090/s0025-5718-1987-0866103-4openalex-snapshot
Class Groups of Number Fields: Numerical Heuristics
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