Results 51 to 60 of about 217 (158)
On the linear complexity of a new generalized cyclotomic sequence with length mover GF(h)
Tongxin xuebao, 2017 Based on the Ding-generalized cyclotomy,a new class of generalized cyclotomic sequences with length pm over the finite field of power of odd prime order was constructed,and the sequence was balanced.The linear complexity of the sequences was determined ...
Long-fei LIU, Kai YANG, Xiao-yuan YANG
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STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE
Forum of Mathematics, Pi, 2015 Let $E$ be an elliptic curve over $\mathbb{Q}$, and let ${\it\varrho}_{\flat }$ and ${\it\varrho}_{\sharp }$ be odd two-dimensional Artin representations for which ${\it\varrho}_{\flat }\otimes {\it\varrho}_{\sharp }$ is self-dual.
HENRI DARMON, ALAN LAUDER, VICTOR ROTGER
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On the class numbers of cyclotomic fields
Manuscripta Mathematica, 1989 The class number h of a cyclotomic field factors as \(h=h^+h^-\), where \(h^+\) is the class number of the maximal real subfield and \(h^-\) is an integer called the relative class number. The author shows that there are only finitely many cyclotomic fields K such that the odd part of \(h^-_ K\) is below a given bound. The proof uses a nice combination
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On the class numbers of real cyclotomic fields of conductor pq [PDF]
Acta Arithmetica, 2014 The class numbers $h^{+}$ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power.
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Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p$p$
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let G$G$ be a finite group and p$p$ be a prime. We establish an upper bound for the derived length of a Sylow p$p$‐subgroup of G$G$ in terms of the number of irreducible characters of G$G$ whose degrees are divisible by p$p$. We also prove that if B$B$ is a p$p$‐block of a finite p$p$‐solvable group G$G$ with defect group D$D$, then the ...
James P. Cossey +3 more
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The class number of cyclotomic function fields
Journal of Number Theory, 1981 AbstractLet k be a rational function field over a finite field. Carlitz and Hayes have described a family of extensions of k which are analogous to the collection of cyclotomic extensions {Q(ζm)| m ≥ 2} of the rational field Q. We investigate arithmetic properties of these “cyclotomic function fields.” We introduce the notion of the maximal real ...
Galovich, Steven, Rosen, Michael
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Class numbers of cyclotomic function fields [PDF]
Acta Arithmetica, 2002 Let \(A={\mathbb{F}}_q[T]\) be the ring of polynomials over a finite field \({\mathbb{F}} _q\) of \(q\) elements. Let \(k = {\mathbb{F}}_q (T)\) be the rational function field over \({\mathbb{F}}_q\). For \(M\in A\) let \(k\big(\Lambda _M\big)\) be the \(M\)-th Carlitz-Hayes cyclotomic function field.
Bae, Sunghan, Kang, Pyung-Lyun
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Abelian threefolds with imaginary multiplication
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract Let A$A$ be an abelian threefold defined over a number field K$K$ with potential multiplication by an imaginary quadratic field M$M$. Under mild assumptions on K$K$, if A$A$ has signature (2,1) and the multiplication by M$M$ is defined over KM$KM$, we attach to A$A$ an elliptic curve defined over K$K$ with potential complex multiplication by M$
Francesc Fité, Pip Goodman
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On the Lang–Trotter conjecture for Siegel modular forms
Mathematika, Volume 72, Issue 3, July 2026.Abstract Let f$f$ be a genus‐two cuspidal Siegel eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated with f$f$, generalizing the results of Ribet and Momose for elliptic modular forms. Using this result, we investigate the distribution of the Hecke eigenvalues ap$a_p$ of f$f$, and obtain upper
Arvind Kumar, Moni Kumari, Ariel Weiss
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Class numbers of cyclotomic function fields [PDF]
Transactions of the American Mathematical Society, 1999 Let q q be a prime power and let
Guo, Li, Shu, Linghsueh
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