Results 1 to 10 of about 494 (41)
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 the prime divisors of elements of a $D(-1)$ quadruple [PDF]
, 2013 We show that if {1, b, c, d} is a D(-1) diophantine quadruple with ...
Anitha Srinivasan, Filipin, Ribenboim
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Stickelberger's congruences for absolute norms of relative discriminants [PDF]
, 2010 We give an improvement of a result of J. Martinet on Stickelberger's congruences for the absolute norms of relative discriminants of number fields, by using classical arguments of class field ...
Gras, Georges
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Some Questions on the Ideal Class Group of Imaginary Abelian Fields [PDF]
, 2007 Let k be an imaginary quadratic field. Assume that the class number of k is exactly an odd prime number p, and p splits into two distinct primes in k. Then it is known that a prime ideal lying above p is not principal.
Itoh, Tsuyoshi
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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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On The Relative Class Number of Special Cyclotomic Fields [PDF]
, 2012 Let p be an odd prime, p be a primitive pth root of unity and h p be the relative class number of the pth cyclotomic fi eld Q( p) over the rationals Q defi ned by p.
Agoh, Takashi
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Class number formulas via 2-isogenies of elliptic curves [PDF]
, 2012 A classical result of Dirichlet shows that certain elementary character sums compute class numbers of quadratic imaginary number fields. We obtain analogous relations between class numbers and a weighted character sum associated to a 2-isogeny of ...
McLeman, Cam, Rasmussen, Christopher
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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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The minimum discriminant of number fields of degree 8 and signature (2,3)
, 2018 In this paper we describe how to use the algorithmic methods provided by Hunter and Pohst in order to give a complete classification of number fields of degree 8 and signature (2,3) with absolute discriminant less than a certain bound. The choice of this
Battistoni, Francesco
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A counterexample to 'Algebraic function fields with small class number' [PDF]
, 2013 I give a counter example of function field over GF(2) of genus 4 with class number one.
Stirpe, Claudio
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