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Maximilian F. Hasler

Publications and source records attributed to Maximilian F. Hasler.

8 recordsLinked to original sources
arXiv2018

Primitive weird numbers having more than three distinct prime factors

In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a given number of distinct prime factors are presented. These algorithms yield primitive weird numbers of the form $mp_1\dots p_k$ for a suitable deficient positive integer $m$ and primes $p_1,\dots,p_k$ and generalize a recent technique developed for generating primitive weird numbers of the form $2^np_1p_2$. The same techniques can be used to search for odd weird numbers, whose existence is still an open question.

math.NT↗
arXiv2018

Primitive abundant and weird numbers with many prime factors

We give an algorithm to enumerate all primitive abundant numbers (briefly, PANs) with a fixed $Ω$ (the number of prime factors counted with their multiplicity), and explicitly find all PANs up to $Ω=6$, count all PANs and square-free PANs up to $Ω=7$ and count all odd PANs and odd square-free PANs up to $Ω=8$. We find primitive weird numbers (briefly, PWNs) with up to 16 prime factors, improving the previous results of [Amato-Hasler-Melfi-Parton] where PWNs with up to 6 prime factors have been given. The largest PWN we find has 14712 digits: as far as we know, this is the largest example existing, the previous one being 5328 digits long [Melfi]. We find hundreds of PWNs with exactly one square odd prime factor: as far as we know, only five were known before. We find all PWNs with at least one odd prime factor with multiplicity greater than one and $Ω= 7$ and prove that there are none with $Ω< 7$. Regarding PWNs with a cubic (or higher) odd prime factor, we prove that there are none with $Ω\le 7$, and we did not find any with larger $Ω$. Finally, we find several PWNs with 2 square odd prime factors, and one with 3 square odd prime factors. These are the first such examples.

math.NT↗
arXiv2007

Generalized functions as sequence spaces with ultranorms

We review our recent formulation of Colombeau type algebras as Hausdorff sequence spaces with ultranorms, defined by sequences of exponential weights. We extend previous results and give new perspectives related to echelon type spaces, possible generalisations, asymptotic algebras, concepts of association, and applications thereof.

math.FA↗
arXiv2002

Embeddings of ultradistributions and periodic hyperfunctions in Colombeau type algebras through sequence spaces

In a recent paper, we gave a topological description of Colombeau type algebras introducing algebras of sequences with exponential weights. Embeddings of Schwartz' spaces into the Colombeau algebra G are well known, but for ultradistribution and periodic hyperfunction type spaces we give new constructions. We show that the multiplication of regular enough functions (smooth, ultradifferentiable or quasianalytic), embedded into corresponding algebras, is the ordinary multiplication.

math.FA↗
arXiv2002

Generalized function algebras as sequence space algebras

A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac's delta distribution induces discrete topology on the basic space. This result is in analogy to Schwartz' impossibility result concerning multiplication of distributions.

math.FA↗
arXiv1997

The three-form multiplet in N=2 superspace

We present an N=2 multiplet including a three-index antisymmetric tensor gauge potential, and describe it as a solution to the Bianchi identities for the associated fieldstrength superform, subject to some covariant constraints, in extended central charge superspace. We find that this solution is given in terms of an 8+8 tensor multiplet subject to an additional constraint. We give the transformation laws for the multiplet as well as invariant superfield and component field lagrangians, and mention possible couplings to other multiplets. We also allude to the relevance of the 3--form geometry for generic invariant supergravity actions.

hep-th↗