Results 31 to 40 of about 11,330 (177)
ON WEIL NUMBERS IN CYCLOTOMIC FIELDS [PDF]
International Journal of Number Theory, 2009 In this paper, we study the p-adic behavior of Weil numbers in the cyclotomic ℤp-extension of the pth cyclotomic field. We determine the characteristic ideal of the quotient of semi-local units by Weil numbers in terms of the characteristic ideals of some classical modules that appear in the Iwasawa theory.
Anglès, Bruno, Beliaeva, Tatiana
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Endomorphisms of abelian varieties, cyclotomic extensions and Lie algebras
, 2010 We prove an analogue of the Tate conjecture on homomorphisms of abelian varieties over infinite cyclotomic extensions of finitely generated fields of characteristic zero.Comment: 9 ...
Ch. W. Curtis +19 more
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A Note on Factorization and the Number of Irreducible Factors of xn − λ over Finite Fields
MathematicsLet Fq be a finite field, and let n be a positive integer such that gcd(q,n)=1. The irreducible factors of xn−1 and xn−λ are fundamental concepts with wide applications in cyclic codes and constacyclic codes.
Jinle Liu, Hongfeng Wu
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On the failure of pseudo-nullity of Iwasawa modules
, 2004 We consider the family of CM-fields which are pro-p p-adic Lie extensions of number fields of dimension at least two, which contain the cyclotomic Z_p-extension, and which are ramified at only finitely many primes.
Romyar, T. Sharifi, Yoshitaka Hachimori
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Factor-4 and 6 compression of cyclotomic subgroups of and
Journal of Mathematical Cryptology, 2010 Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields 𝔽2m and 𝔽3m, respectively, have been used to implement pairing-based cryptographic protocols.
Karabina Koray
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Complementary dual abelian codes in group algebras of some finite abelian groups [PDF]
ITM Web of ConferencesLinear complementary dual codes have become an interesting sub-family of linear codes over finite fields since they can be practically applied in various fields such as cryptography and quantum error-correction. Recently, properties of complementary dual
Jitman Somphong
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Ideal class groups of cyclotomic number fields II [PDF]
, 1995 We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields.
Lemmermeyer, Franz
core
A P‐adic class formula for Anderson t‐modules
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In 2012, Taelman proved a class formula for L$L$‐series associated to Drinfeld Fq[θ]$\mathbb {F}_q[\theta]$‐modules and considered it as a function field analogue of the Birch and Swinnerton‐Dyer conjecture. Since then, Taelman's class formula has been generalized to the setting of Anderson t$t$‐modules.
Alexis Lucas
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EULER–KRONECKER CONSTANTS FOR CYCLOTOMIC FIELDS
Bulletin of the Australian Mathematical Society, 2022 AbstractThe Euler–Mascheroni constant $\gamma =0.5772\ldots \!$ is the $K={\mathbb Q}$ example of an Euler–Kronecker constant $\gamma _K$ of a number field $K.$ In this note, we consider the size of the $\gamma _q=\gamma _{K_q}$ for cyclotomic fields $K_q:={\mathbb Q}(\zeta _q).$ Assuming the Elliott–Halberstam Conjecture (EH), we prove ...
Hong, Letong, Ono, Ken, Zhang, Shengtong
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Ordinary primes for GL2$\operatorname{GL}_2$‐type abelian varieties and weight 2 modular forms
Mathematika, Volume 72, Issue 2, April 2026.Abstract Let A$A$ be a g$g$‐dimensional abelian variety defined over a number field F$F$. It is conjectured that the set of ordinary primes of A$A$ over F$F$ has positive density, and this is known to be true when g=1,2$g=1, 2$, or for certain abelian varieties with extra endomorphisms.
Tian Wang, Pengcheng Zhang
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