Related papers: The L-functions and modular forms database project
We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…
The Langlands-Shelstad transfer factor is a function defined on some reductive groups over a p-adic field. Near the origin of the group, it may be viewed as a function on the Lie algebra. For classical groups, its values have the form q^c…
Large language models (LLMs) offer new opportunities for automated data extraction and property prediction across materials science, yet their use in superconductivity research remains limited. Here we construct a large experimental…
Federated learning (FL) represents a novel paradigm to machine learning, addressing critical issues related to data privacy and security, yet suffering from data insufficiency and imbalance. The emergence of foundation models (FMs) provides…
This is an overview of Erlangen Programme at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the…
We derive a family of approximations for L-functions of Hecke cusp eigenforms, according to a recipe first described by Matiyasevich for the Riemann xi function. We show that these approximations converge to the true L-function and point…
Dependently typed lambda calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic…
This paper aims at the problem of link pattern prediction in collections of objects connected by multiple relation types, where each type may play a distinct role. While common link analysis models are limited to single-type link…
Dirichlet's $L$-functions are natural extensions of the Riemann zeta function. In this paper we first give a brief survey of Ap\'ery-like series for some special values of the zeta function and certain $L$-functions. Then, we establish two…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
This book is based on notes compiled over the many years I have been teaching the course "Applied Functional Analysis" in the first year of the Master programme at Delft University of Technology, for students with previous exposure to the…
This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
In the rapidly evolving AI era with large language models (LLMs) at the core, making LLMs more trustworthy and efficient, especially in output generation (inference), has gained significant attention. This is to reduce plausible but faulty…
We introduce a natural definition for sums of the form \[ \sum_{\nu=1}^x f(\nu) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…
Multi-modal Large Language Models (MLLMs) have exhibited impressive capability. However, recently many deficiencies of MLLMs have been found compared to human intelligence, $\textit{e.g.}$, hallucination. To drive the MLLMs study, the…
The rapid development of large language models (LLMs) has been witnessed in recent years. Based on the powerful LLMs, multi-modal LLMs (MLLMs) extend the modality from text to a broader spectrum of domains, attracting widespread attention…
The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is fundamental to the study and simulation of fractional differential and integral equations. However, these functions are computationally expensive and their numerical…
While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants…