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This paper deals with a continuous analogon to irregularities of point distributions. If a continuous fonction $x : [0, 1] \to X$ where $X$ is a compact body, is interpreted as a particle’s movement in time, then the discrepancy measures the difference between the particle’s stay in a proper subset and the volume of the subset. The essential part of this paper is to give lower bounds for the discrepancy in terms of the arc length of $x (t)$ , $0 \leq t \leq 1$ . Furthermore it is shown that these estimates are the best possible despite of...

Irregularities of Distribution. IV.

W.M. SCHMIDT (1969)

Inventiones mathematicae

Irregularities of distribution of digital $0, 1$ -sequences in prime base.

Faure, Henri (2005)

Integers

Irregularities of distribution. VI

Wolfgang M. Schmidt (1972)

Compositio Mathematica

Irregularities of distribution, VII

Wolfgang Schmidt (1972)

Acta Arithmetica

Irregularities of Point Distributions Relative to Homothetic Convex Bodies I.

Gyula Károlyi (1995)

Monatshefte für Mathematik

Irregularity and $p$ -adic Swan conductor. (Irrégularité et conducteur de Swan $p$ -adiques.)

Marmora, Adriano (2004)

Documenta Mathematica

Isogenies of prime degree over number fields

Fumiyuki Momose (1995)

Compositio Mathematica

Isogeny orbits in a family of abelian varieties

Qian Lin, Ming-Xi Wang (2015)

Acta Arithmetica

We prove that if a curve of a nonisotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety, then it is either torsion or contained in a fiber. This result fits into the context of the Zilber-Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.

Isometries of quadratic spaces

Eva Bayer-Fluckiger (2015)

Journal of the European Mathematical Society

Let $k$ be a global field of characteristic not 2, and let $f \in k [X]$ be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial $f$ if and only if such an isometry exists over all the completions of $k$ . This gives a partial answer to a question of Milnor.

Isomorphic digraphs from powers modulo $p$

Guixin Deng, Pingzhi Yuan (2011)

Czechoslovak Mathematical Journal

Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_{p}^{k}$ whose set of vertices is ${1, 2, ..., p - 1}$ and there exists a directed edge from a vertex $a$ to a vertex $b$ if $a^{k} \equiv b (mod p)$ . In this paper we obtain a necessary and sufficient condition for $G_{p}^{k_{1}} ≃ G_{p}^{k_{2}}$ .

Isomorphisms of algebraic number fields

Mark van Hoeij, Vivek Pal (2012)

Journal de Théorie des Nombres de Bordeaux

Let $ℚ (α)$ and $ℚ (β)$ be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, $ℚ (β) \to ℚ (α)$ . The algorithm is particularly efficient if there is only one isomorphism.

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Irregular Primes and Integrality Theorems for Manifolds.

Irrégularités dans la distribution des nombres premiers dans les progressions arithmétiques

Irregularities for distribution IX

Irregularities in the distribution of primes in an arithmetic progression

Irregularities in the distribution of primes in short intervals.

Irregularities of continuous distributions