Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: MSC category 11 ( Number theory )

 Expand all        Collapse all Results 151 - 175 of 207

151. CMB 2002 (vol 45 pp. 196)

Dubickas, Artūras
 Mahler Measures Close to an Integer We prove that the Mahler measure of an algebraic number cannot be too close to an integer, unless we have equality. The examples of certain Pisot numbers show that the respective inequality is sharp up to a constant. All cases when the measure is equal to the integer are described in terms of the minimal polynomials. Keywords:Mahler measure, PV numbers, Salem numbersCategories:11R04, 11R06, 11R09, 11J68

152. CMB 2002 (vol 45 pp. 220)

Hakim, Jeffrey; Murnaghan, Fiona
 Globalization of Distinguished Supercuspidal Representations of $\GL(n)$ An irreducible supercuspidal representation $\pi$ of $G= \GL(n,F)$, where $F$ is a nonarchimedean local field of characteristic zero, is said to be distinguished'' by a subgroup $H$ of $G$ and a quasicharacter $\chi$ of $H$ if $\Hom_H(\pi,\chi)\noteq 0$. There is a suitable global analogue of this notion for and irreducible, automorphic, cuspidal representation associated to $\GL(n)$. Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. Applications to the theory of distinguished supercuspidal representations are provided. Categories:22E50, 22E35, 11F70

153. CMB 2002 (vol 45 pp. 257)

Lee, Min Ho
 Modular Forms Associated to Theta Functions We use the theory of Jacobi-like forms to construct modular forms for a congruence subgroup of $\SL(2,\mathbb{R})$ which can be expressed as linear combinations of products of certain theta functions. Categories:11F11, 11F27, 33D10

154. CMB 2002 (vol 45 pp. 247)

Kihel, O.; Levesque, C.
 On a Few Diophantine Equations Related to Fermat's Last Theorem We combine the deep methods of Frey, Ribet, Serre and Wiles with some results of Darmon, Merel and Poonen to solve certain explicit diophantine equations. In particular, we prove that the area of a primitive Pythagorean triangle is never a perfect power, and that each of the equations $X^4 - 4Y^4 = Z^p$, $X^4 + 4Y^p = Z^2$ has no non-trivial solution. Proofs are short and rest heavily on results whose proofs required Wiles' deep machinery. Keywords:Diophantine equationsCategory:11D41

155. CMB 2002 (vol 45 pp. 123)

Moody, Robert V.
 Uniform Distribution in Model Sets We give a new measure-theoretical proof of the uniform distribution property of points in model sets (cut and project sets). Each model set comes as a member of a family of related model sets, obtained by joint translation in its ambient (the `physical') space and its internal space. We prove, assuming only that the window defining the model set is measurable with compact closure, that almost surely the distribution of points in any model set from such a family is uniform in the sense of Weyl, and almost surely the model set is pure point diffractive. Categories:52C23, 11K70, 28D05, 37A30

156. CMB 2002 (vol 45 pp. 115)

Luca, Florian
 The Number of Non-Zero Digits of $n!$ Let $b$ be an integer with $b>1$. In this note, we prove that the number of non-zero digits in the base $b$ representation of $n!$ grows at least as fast as a constant, depending on $b$, times $\log n$. Category:11A63

157. CMB 2002 (vol 45 pp. 86)

Gerth, Frank
 On Cyclic Fields of Odd Prime Degree $p$ with Infinite Hilbert $p$-Class Field Towers Let $k$ be a cyclic extension of odd prime degree $p$ of the field of rational numbers. If $t$ denotes the number of primes that ramify in $k$, it is known that the Hilbert $p$-class field tower of $k$ is infinite if $t>3+2\sqrt p$. For each $t>2+\sqrt p$, this paper shows that a positive proportion of such fields $k$ have infinite Hilbert $p$-class field towers. Categories:11R29, 11R37, 11R45

158. CMB 2002 (vol 45 pp. 97)

Haas, Andrew
 Invariant Measures and Natural Extensions We study ergodic properties of a family of interval maps that are given as the fractional parts of certain real M\"obius transformations. Included are the maps that are exactly $n$-to-$1$, the classical Gauss map and the Renyi or backward continued fraction map. A new approach is presented for deriving explicit realizations of natural automorphic extensions and their invariant measures. Keywords:Continued fractions, interval maps, invariant measuresCategories:11J70, 58F11, 58F03

159. CMB 2002 (vol 45 pp. 138)

Spearman, Blair K.; Williams, Kenneth S.
 The Discriminant of a Dihedral Quintic Field Defined by a Trinomial $X^5 + aX + b$ Let $X^5 + aX + b \in Z[X]$ have Galois group $D_5$. Let $\theta$ be a root of $X^5 + aX + b$. An explicit formula is given for the discriminant of $Q(\theta)$. Keywords:dihedral quintic field, trinomial, discriminantCategories:11R21, 11R29

160. CMB 2002 (vol 45 pp. 109)

Hall, R. R.; Shiu, P.
 The Distribution of Totatives D.~H.~Lehmer initiated the study of the distribution of totatives, which are numbers coprime with a given integer. This led to various problems considered by P.~Erd\H os, who made a conjecture on such distributions. We prove his conjecture by establishing a theorem on the ordering of residues. Keywords:Euler's function, totativesCategories:11A05, 11A07, 11A25

161. CMB 2002 (vol 45 pp. 36)

Cummins, C. J.
 Modular Equations and Discrete, Genus-Zero Subgroups of $\SL(2,\mathbb{R})$ Containing $\Gamma(N)$ Let $G$ be a discrete subgroup of $\SL(2,\R)$ which contains $\Gamma(N)$ for some $N$. If the genus of $X(G)$ is zero, then there is a unique normalised generator of the field of $G$-automorphic functions which is known as a normalised Hauptmodul. This paper gives a characterisation of normalised Hauptmoduls as formal $q$ series using modular polynomials. Categories:11F03, 11F22, 30F35

162. CMB 2001 (vol 44 pp. 398)

Cardon, David A.; Ram Murty, M.
 Exponents of Class Groups of Quadratic Function Fields over Finite Fields We find a lower bound on the number of imaginary quadratic extensions of the function field $\F_q(T)$ whose class groups have an element of a fixed order. More precisely, let $q \geq 5$ be a power of an odd prime and let $g$ be a fixed positive integer $\geq 3$. There are $\gg q^{\ell (\frac{1}{2}+\frac{1}{g})}$ polynomials $D \in \F_q[T]$ with $\deg(D) \leq \ell$ such that the class groups of the quadratic extensions $\F_q(T,\sqrt{D})$ have an element of order~$g$. Keywords:class number, quadratic function fieldCategories:11R58, 11R29

163. CMB 2001 (vol 44 pp. 440)

Hironaka, Eriko
 The Lehmer Polynomial and Pretzel Links In this paper we find a formula for the Alexander polynomial $\Delta_{p_1,\dots,p_k} (x)$ of pretzel knots and links with $(p_1,\dots,p_k, \nega 1)$ twists, where $k$ is odd and $p_1,\dots,p_k$ are positive integers. The polynomial $\Delta_{2,3,7} (x)$ is the well-known Lehmer polynomial, which is conjectured to have the smallest Mahler measure among all monic integer polynomials. We confirm that $\Delta_{2,3,7} (x)$ has the smallest Mahler measure among the polynomials arising as $\Delta_{p_1,\dots,p_k} (x)$. Keywords:Alexander polynomial, pretzel knot, Mahler measure, Salem number, Coxeter groupsCategories:57M05, 57M25, 11R04, 11R27

164. CMB 2001 (vol 44 pp. 385)

Ballantine, Cristina M.
 A Hypergraph with Commuting Partial Laplacians Let $F$ be a totally real number field and let $\GL_{n}$ be the general linear group of rank $n$ over $F$. Let $\mathfrak{p}$ be a prime ideal of $F$ and $F_{\mathfrak{p}}$ the completion of $F$ with respect to the valuation induced by $\mathfrak{p}$. We will consider a finite quotient of the affine building of the group $\GL_{n}$ over the field $F_{\mathfrak{p}}$. We will view this object as a hypergraph and find a set of commuting operators whose sum will be the usual adjacency operator of the graph underlying the hypergraph. Keywords:Hecke operators, buildingsCategories:11F25, 20F32

165. CMB 2001 (vol 44 pp. 282)

Lee, Min Ho; Myung, Hyo Chul
 Hecke Operators on Jacobi-like Forms Jacobi-like forms for a discrete subgroup $\G \subset \SL(2,\mbb R)$ are formal power series with coefficients in the space of functions on the Poincar\'e upper half plane satisfying a certain functional equation, and they correspond to sequences of certain modular forms. We introduce Hecke operators acting on the space of Jacobi-like forms and obtain an explicit formula for such an action in terms of modular forms. We also prove that those Hecke operator actions on Jacobi-like forms are compatible with the usual Hecke operator actions on modular forms. Categories:11F25, 11F12

166. CMB 2001 (vol 44 pp. 313)

Reverter, Amadeu; Vila, Núria
 Images of mod $p$ Galois Representations Associated to Elliptic Curves We give an explicit recipe for the determination of the images associated to the Galois action on $p$-torsion points of elliptic curves. We present a table listing the image for all the elliptic curves defined over $\QQ$ without complex multiplication with conductor less than 200 and for each prime number~$p$. Keywords:Galois groups, elliptic curves, Galois representation, isogenyCategories:11R32, 11G05, 12F10, 14K02

167. CMB 2001 (vol 44 pp. 242)

Schueller, Laura Mann
 The Zeta Function of a Pair of Quadratic Forms The zeta function of a nonsingular pair of quadratic forms defined over a finite field, $k$, of arbitrary characteristic is calculated. A.~Weil made this computation when $\rmchar k \neq 2$. When the pair has even order, a relationship between the number of zeros of the pair and the number of places of degree one in an appropriate hyperelliptic function field is Category:11G25

168. CMB 2001 (vol 44 pp. 160)

Langlands, Robert P.
 The Trace Formula and Its Applications: An Introduction to the Work of James Arthur James Arthur was awarded the Canada Gold Medal of the National Science and Engineering Research Council in 1999. This introduction to his work is an attempt to explain his methods and his goals to the mathematical community at large. Categories:11F70, 11F72, 58G25

169. CMB 2001 (vol 44 pp. 3)

Alexandru, Victor; Popescu, Nicolae; Zaharescu, Alexandru
 The Generating Degree of $\C_p$ The generating degree $\gdeg (A)$ of a topological commutative ring $A$ with $\Char A = 0$ is the cardinality of the smallest subset $M$ of $A$ for which the subring $\Z[M]$ is dense in $A$. For a prime number $p$, $\C_p$ denotes the topological completion of an algebraic closure of the field $\Q_p$ of $p$-adic numbers. We prove that $\gdeg (\C_p) = 1$, \ie, there exists $t$ in $\C_p$ such that $\Z[t]$ is dense in $\C_p$. We also compute $\gdeg \bigl( A(U) \bigr)$ where $A(U)$ is the ring of rigid analytic functions defined on a ball $U$ in $\C_p$. If $U$ is a closed ball then $\gdeg \bigl( A(U) \bigr) = 2$ while if $U$ is an open ball then $\gdeg \bigl( A(U) \bigr)$ is infinite. We show more generally that $\gdeg \bigl( A(U) \bigr)$ is finite for any {\it affinoid} $U$ in $\PP^1 (\C_p)$ and $\gdeg \bigl( A(U) \bigr)$ is infinite for any {\it wide open} subset $U$ of $\PP^1 (\C_p)$. Category:11S99

170. CMB 2001 (vol 44 pp. 12)

Anisca, Razvan; Ilie, Monica
 A Technique of Studying Sums of Central Cantor Sets This paper is concerned with the structure of the arithmetic sum of a finite number of central Cantor sets. The technique used to study this consists of a duality between central Cantor sets and sets of subsums of certain infinite series. One consequence is that the sum of a finite number of central Cantor sets is one of the following: a finite union of closed intervals, homeomorphic to the Cantor ternary set or an $M$-Cantorval. Category:11B05

171. CMB 2001 (vol 44 pp. 22)

Evans, Ronald
 Gauss Sums of Orders Six and Twelve Precise, elegant evaluations are given for Gauss sums of orders six and twelve. Categories:11L05, 11T24

172. CMB 2001 (vol 44 pp. 87)

Lieman, Daniel; Shparlinski, Igor
 On a New Exponential Sum Let $p$ be prime and let $\vartheta\in\Z^*_p$ be of multiplicative order $t$ modulo $p$. We consider exponential sums of the form $$S(a) = \sum_{x =1}^{t} \exp(2\pi i a \vartheta^{x^2}/p)$$ and prove that for any $\varepsilon > 0$ $$\max_{\gcd(a,p) = 1} |S(a)| = O( t^{5/6 + \varepsilon}p^{1/8}) .$$ Categories:11L07, 11T23, 11B50, 11K31, 11K38

173. CMB 2001 (vol 44 pp. 115)

Roy, Damien
 Approximation algÃ©brique simultanÃ©e de nombres de Liouville The purpose of this paper is to show the limitations of the conjectures of algebraic approximation. For this, we construct points of $\bC^m$ which do not admit good algebraic approximations of bounded degree and height, when the bounds on the degree and the height are taken from specific sequences. The coordinates of these points are Liouville numbers. Category:11J82

174. CMB 2001 (vol 44 pp. 97)

Ou, Zhiming M.; Williams, Kenneth S.
 On the Density of Cyclic Quartic Fields An asymptotic formula is obtained for the number of cyclic quartic fields over $Q$ with discriminant $\leq x$. Keywords:cyclic quartic fields, density, discriminantCategories:11R16, 11R29

175. CMB 2001 (vol 44 pp. 19)

Brindza, B.; Pintér, Á.; Schmidt, W. M.
 Multiplicities of Binary Recurrences In this note the multiplicities of binary recurrences over algebraic number fields are investigated under some natural assumptions. Categories:11B37, 11J86
 Page Previous 1 ... 6 7 8 9 Next

© Canadian Mathematical Society, 2014 : https://cms.math.ca/