Multiplicative functions dictated by Artin symbols

Robert J. Lemke Oliver

The search session has expired. Please query the service again.

Displaying similar documents to “Multiplicative functions dictated by Artin symbols”

Counting discriminants of number fields

Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

For each transitive permutation group $G$ on $n$ letters with $n \leq 4$ , we give without proof results, conjectures, and numerical computations on discriminants of number fields $L$ of degree $n$ over $ℚ$ such that the Galois group of the Galois closure of $L$ is isomorphic to $G$ .

Radii of p-valence of certain analytic functions of order $α$ with negative coefficients

M. K. Aouf (1989)

Matematički Vesnik

Similarity:

On the $k$ -polygonal numbers and the mean value of Dedekind sums

Jing Guo, Xiaoxue Li (2016)

Czechoslovak Mathematical Journal

Similarity:

For any positive integer $k \geq 3$ , it is easy to prove that the $k$ -polygonal numbers are $a_{n} (k) = (2 n + n (n - 1) (k - 2)) / 2$ . The main purpose of this paper is, using the properties of Gauss sums and Dedekind sums, the mean square value theorem of Dirichlet $L$ -functions and the analytic methods, to study the computational problem of one kind mean value of Dedekind sums $S (a_{n} (k) {\bar{a}}_{m} (k), p)$ for $k$ -polygonal numbers with $1 \leq m, n \leq p - 1$ , and give an interesting computational formula for it.

Random Galois extensions of Hilbertian fields

Lior Bary-Soroker, Arno Fehm (2013)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $L$ be a Galois extension of a countable Hilbertian field $K$ . Although $L$ need not be Hilbertian, we prove that an abundance of large Galois subextensions of $L / K$ are.

Arithmetic Properties of Generalized Rikuna Polynomials

Z. Chonoles, J. Cullinan, H. Hausman, A.M. Pacelli, S. Pegado, F. Wei (2014)

Publications mathématiques de Besançon

Similarity:

Fix an integer $ℓ \geq 3$ . Rikuna introduced a polynomial $r (x, t)$ defined over a function field $K (t)$ whose Galois group is cyclic of order $ℓ$ , where $K$ satisfies some mild hypotheses. In this paper we define the family of ${r_{n} (x, t)}_{n \geq 1}$ of degree $ℓ^{n}$ . The $r_{n} (x, t)$ are constructed iteratively from the $r (x, t)$ . We compute the Galois groups of the $r_{n} (x, t)$ for odd $ℓ$ over an arbitrary base field and give applications to arithmetic dynamical systems.

Divisors in global analytic sets

Francesca Acquistapace, A. Díaz-Cano (2011)

Journal of the European Mathematical Society

Similarity:

We prove that any divisor $Y$ of a global analytic set $X \subset ℝ^{n}$ has a generic equation, that is, there is an analytic function vanishing on $Y$ with multiplicity one along each irreducible component of $Y$ . We also prove that there are functions with arbitrary multiplicities along $Y$ . The main result states that if $X$ is pure dimensional, $Y$ is locally principal, $X / Y$ is not connected and $Y$ represents the zero class in $H_{q - 1}^{\infty} (X, ℤ_{2})$ then the divisor $Y$ is globally principal.

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

Jagannath Patel, Ashok Kumar Sahoo (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class $R^{λ} (a, c, A, B)$ of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass ${\tilde{R}}^{λ} (a, c, A, B)$ of $R^{λ} (a, c, A, B)$ and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.

Proof of a conjectured three-valued family of Weil sums of binomials

Daniel J. Katz, Philippe Langevin (2015)

Acta Arithmetica

Similarity:

We consider Weil sums of binomials of the form $W_{F, d} (a) = \sum_{x \in F} ψ (x^{d} - a x)$ , where F is a finite field, ψ: F → ℂ is the canonical additive character, $g c d (d, | F^{\times} |) = 1$ , and $a \in F^{\times}$ . If we fix F and d, and examine the values of $W_{F, d} (a)$ as a runs through $F^{\times}$ , we always obtain at least three distinct values unless d is degenerate (a power of the characteristic of F modulo $| F^{\times} |$ ). Choices of F and d for which we obtain only three values are quite rare and desirable in a wide variety of applications. We show that if F is a field of order 3ⁿ with n...

Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $C^{n}$

J. Siciak (1969)

Annales Polonici Mathematici

Similarity:

On generalized square-full numbers in an arithmetic progression

Angkana Sripayap, Pattira Ruengsinsub, Teerapat Srichan (2022)

Czechoslovak Mathematical Journal

Similarity:

Let $a$ and $b \in ℕ$ . Denote by $R_{a, b}$ the set of all integers $n > 1$ whose canonical prime representation $n = p_{1}^{α_{1}} p_{2}^{α_{2}} \dots p_{r}^{α_{r}}$ has all exponents $α_{i}$ $(1 \leq i \leq r)$ being a multiple of $a$ or belonging to the arithmetic progression $a t + b$ , $t \in ℕ_{0} : = ℕ \cup {0}$ . All integers in $R_{a, b}$ are called generalized square-full integers. Using the exponent pair method, an upper bound for character sums over generalized square-full integers is derived. An application on the distribution of generalized square-full integers in an arithmetic progression is given. ...