Related papers: Admissible Dirichlet Series
In this note, we give examples of formal power series satisfying certain conditions that cannot be realized as Hilbert series of finitely generated modules. This answers to the negative a question raised in a recent article by the second…
In this paper we introduce and study the notion of I-convergence of sequences in a metric-like space, where I is an ideal of subsets of the set N of all natural numbers. Further introducing the notion of I*-convergence of sequences in a…
In a recent paper, Gonek, Graham, and Lee introduced a notion of the Lindel\"of hypothesis (LH) for general sequences which coincides with the usual Lindel\"of hypothesis for the Riemann zeta function in the case of the sequence of positive…
In the current paper we attempt to transfer the notion of the projectional entropy, originally defined for multidimensional subshifts, to the case of actions of amenable groups. The main theorem states that if a system is strongly…
We consider the explicit fragment of the basic justification stit logic introduced in earlier publications. We define a Hilbert-style axiomatic system for this logic and show that this system is strongly complete relative to the intended…
We present results for infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-, two- and three-dimensional series. All these series can be expressed in terms of…
The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic $DL(\partial_{||})$ introduced new…
A new definition for the notion of a (general) $\infty$-category is given.
We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of…
Explainability is one of the key ethical concepts in the design of AI systems. However, attempts to operationalize this concept thus far have tended to focus on approaches such as new software for model interpretability or guidelines with…
In this article we consider alternative definitions-descriptions of a set being Infinite within the primitive Axiomatic System of Zermelo.
We determine the Hilbert series of some classes of ideals generated by generic forms of degree two and three, and investigate the difference to the Hilbert series of ideals generated by powers of linear generic forms of the corresponding…
We provide a novel notion of what it means to be interpretable, looking past the usual association with human understanding. Our key insight is that interpretability is not an absolute concept and so we define it relative to a target model,…
In a previous paper, Yakubovich and the author of this article proved that certain shifted combinations of completed Dirichlet series have infinitely many zeros on the critical line. Here we provide some lower bounds for the number of…
In a recent paper of Akhunzhanov and Shatskov the two-dimensional Dirichlet spectrum with respect to Euclidean norm was defined. We consider an analogous definition for arbitrary norms on $\mathbb{R}^2$ and prove that, for each such norm,…
We obtain a series transformation formula involving the classical Hermite polynomials. We then provide a number of applications using appropriate binomial transformations. Several of the new series involve Hermite polynomials and harmonic…
Explainability in time series models is crucial for fostering trust, facilitating debugging, and ensuring interpretability in real-world applications. In this work, we introduce Implet, a novel post-hoc explainer that generates accurate and…
We present a version of arithmetic in all finite types which allows for a definition of equality at higher types for which all congruence are derivable, for which the soundness of the Dialectica interpretation is provable inside the system…
B.C. Berndt evaluated special values of the cotangent Dirichlet series. T. Arakawa studied a generalization of the series, or generalized cotangent Dirichlet series, and gave its transformation formulae. In this paper, we establish an…
We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…