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Showing 1 to 18 of 18 for “"cyclotomic"”.
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On the coefficients of cyclotomic polynomials
Let $\Phi\sb{n}(z)$ denote the $n$th cyclotomic polynomial, given by$$\Phi\sb{n}(z) = {\prod\limits\sbsp{a=1\atop(a,n)=1}{n}}\ (z - \exp(2\pi ia/n)) = {\sum\limits\sbsp{m=0}{\phi(n)}} a(m,n)z\sp{m}.$$It is easily verified that for $n > 1$ $$\Phi\sb{n}(z)={\prod\limits\sb{d\vert …
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An application of Bernoulli polynomials to the theory of cyclotomic fields.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1965
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Applications of Schur rings in algebraic combinatorics: graphs, partial difference sets and cyclotomic schemes
… partial difference sets and (3) investigation of cyclotomic schemes. The first part deals with graphs with commuting adjacency matrices. Here, we give results for commuting regular graphs and discuss the case of non-regular graphs. The second part deals with the construction of partial difference …
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Explicit Factorization of Generalized Cyclotomic Polynomials of Order $2^m 3$ Over a Finite Field $F_q$
We give explicit factorizations of $a$-cyclotomic polynomials of order $2^m 3$, $Q_{2^m3,a}(x)$, over a finite field $F_q$ with $q$ elements where $q$ is a prime power, $m$ is a nonnegative integer and $a$ is a nonnegative element of $F_q$. We use the relation between usual cyclotomic polynomials …
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Trace Problems in Algebraic Number Fields and Applications to Characters of Finite Groups
… unitary conductor, and prove the conjecture for cyclotomic integers with square-free unitary conductor.
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On Coherence and the Geometry of Certain Families of Lattices
… most notably nearly orthogonal lattices, cyclotomic lattices, and cyclic lattices.</p>
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On Morita Equivalences Between KLR Algebras and VV Algebras
… these quotients and explain how they relate to cyclotomic KLR algebras.
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Swan Modules and Elliptic Functions
… group law. He has obtained elliptic analogues of cyclotomic results. The arithmetic nature of elliptic resolvents, the elliptic analogue of the Gauss sum conductor formula and the strength of the elliptic group law being a Lubin-Tate formal group law enabled Taylor to show that the ring of …
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Zeros of P-Adic L-Functions and Densities Relating to Bernoulli Numbers
… p-adic power series used in the study of cyclotomic fields and defined by Iwasawa.
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Iwasawa theory for modular forms at supersingular primes
… of Kato's main conjecture for f over the Zp-cyclotomic extension of Q. In particular, we generalise Kobayashi's main conjecture on p-supersingular elliptic curves over Q with a_p=0, which asserts that Pollack's p-adic L-functions generate the characteristic ideals of some \pm-Selmer groups …
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Topics in Inverse Galois Theory
… Q with an abelian Galois group is contained in a cyclotomic extension, will be discussed using an approach relying on the study of ramified prime ideals. In contrast, a different method will be explored that defines rigid groups to be groups where a selection of conjugacy classes satisfies a …
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On conjectures related to character varieties of knots and Jones polynomials
… of Jones. In this thesis an analogue of Habiro’s cyclotomic equation for the J_n(K; q) is discovered for J_n(K; q; t_1; t_2). An integrality result for the coefficients in this equation is found as a corollary, offering evidence for the conjecture of Berest and Samuelson for all knots. Separately, …
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On Using Graphical Calculi: Centers, Zeroth Hochschild Homology and Possible Compositions of Induction and Restriction Functors in Various Diagrammatical Algebras
… of the induction and restriction functors in the cyclotomic quotients of the NilHecke algebra. We use a computer program to obtain partial results.
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ΠΡΩΤΟΙ ΑΡΙΘΜΟΙ ΚΑΙ ΚΥΚΛΟΤΟΜΙΑ-ΠΡΩΤΟΙ ΑΡΙΘΜΟΙ ΤΗΣ ΜΟΡΦΗΣ Χ + (Χ+1)
… FORMULAE ARE EXTENDED IN CHAPTER 2 BY MEANS OF CYCLOTOMIC CONCEPTS AND COSINE FUNCTIONS. IN CHAPTER 3 THE PRIME AND COMPOSITENUMBERS OF THE FORM X2+(X+1)2 ARE EXAMINED. THEIR STUDY DEPENDS HEAVILY ON THE FOLLOWING THEOREM(SIERPINSKI): THE NUMBER X2+(X+1)2 IS COMPOSITE IF THERE EXIST NATURAL …
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The algebraic K-theory of the chromatic filtration and the telescope conjecture
… TC of this extension. Combining this with the cyclotomic redshift result of Ben-Moshe--Carmeli--Schlank--Yanovski, this implies that the T(2)-local algebraic K-theory of the K(1)-local sphere is not K(2)-local, and hence a counterexample to the height 2 telescope conjecture. We also give …
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Iwasawa theory over solvable three-dimensional p-adic Lie extensions
… the behaviour of ideal class groups over cyclotomic Zp-extensions, and related this to the Kubota-Leopoldt p-adic zeta-function. During the last two decades, the main conjecture has been greatly generalized to admissible p-adic Lie extensions, and provides a conjectural relationship …
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L-invariants and congruences for Galois representations of dimension 3, 4, and 8
… Lₚ(f⊗g) and Lₚ (f⊗g⊗h): the former is cyclotomic in its nature, while the latter is over the weight space. As a corollary, we derive transition formulae relating analytic λ-invariants for pairs of congruent Galois representations for 𝘝𝒻 ⊗ 𝘝𝓰, and for 𝘝𝒻 ⊗ 𝘝𝓰⊗ 𝘝ₕ.