Results 1 to 10 of about 31 (31)
Average value of the divisor class numbers of real cubic function fields
Open Mathematics, 2023 We compute an asymptotic formula for the divisor class numbers of real cubic function fields Km=k(m3){K}_{m}=k\left(\sqrt[3]{m}), where Fq{{\mathbb{F}}}_{q} is a finite field with qq elements, q≡1(mod3)q\equiv 1\hspace{0.3em}\left(\mathrm{mod}\hspace{0 ...
Lee Yoonjin, Lee Jungyun, Yoo Jinjoo
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On class groups of random number fields
Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 927-953, October 2020., 2020 Abstract The main aim of this paper is to disprove the Cohen–Lenstra–Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the probability weights appearing in the general form of the heuristics.
Alex Bartel, Hendrik W. Lenstra Jr.
wiley +1 more source
Capitulation of the 2-ideal classes of type (2, 2, 2) of some quartic cyclic number fields
Journal of Mathematical Cryptology, 2019 Let p≡3(mod4){p\equiv 3\pmod{4}} and l≡5(mod8){l\equiv 5\pmod{8}} be different primes such that pl=1{\frac{p}{l}=1} and 2p=pl4{\frac{2}{p}=\frac{p}{l}_{4}}. Put k=ℚ(l){k=\mathbb{Q}(\sqrt{l})}, and denote by ϵ its fundamental unit. Set K=k(-2pϵl){K=k(
Azizi Abdelmalek +3 more
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A relative integral basis over ℚ(−3) for the normal closure of a pure cubic field
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 25, Page 1623-1626, 2003., 2003 Let K be a pure cubic field. Let L be the normal closure of K. A relative integral basis (RIB) for L over ℚ(−3) is given. This RIB simplifies and completes the one given by Haghighi (1986).
Blair K. Spearman, Kenneth S. Williams
wiley +1 more source
Continued fractions and class number two
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 9, Page 565-571, 2001., 2001 We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm‐induced quadratic polynomial. By doing so, this provides a real quadratic field analogue of the well‐known result by Hendy (1974) for complex quadratic
Richard A. Mollin
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The average size of 3-torsion in class groups of 2-extensions
Forum of Mathematics, PiWe determine the average size of the $3$ -torsion in class groups of G-extensions of a number field when G is any transitive $2$ -group containing a transposition, for example $D_4$ .
Robert Lemke Oliver +2 more
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Criterion for Class Number of the Family Q254m2+m to be Greater Than or Equal to Three
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this paper, we present an explicit lower bound for the class number of real quadratic field k=QD, where D = 25m2 + 4m is a square‐free integer and m ≡ 4 (mod 5) is an odd positive integer.
Ahmad Issa, Huadong Su
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Open MathematicsLet K be an Artin-Schreier extension of the rational function field k≔Fq(T) $k{:=}{\mathbb{F}}_{q}\left(T\right)$ , where Fq ${\mathbb{F}}_{q}$ is a finite field of order q and q is a power of p.
Yoo Jinjoo, Lee Yoonjin
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Neoadjuvant Targeted Therapy in Non-Small Cell Lung Cancer and Its Impact on Surgical Outcomes. [PDF]
Ann Thorac Surg Short Rep, 2023 Sorin M +13 more
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Unit groups of some multiquadratic number fields and 2-class groups. [PDF]
Period Math Hung, 2022 Chems-Eddin MM.
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