Related papers: The L-functions and modular forms database project

The Local Molecular Field Theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation…

The main objective of this article is to present $\nu$-fractional derivative $\mu$-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new $\nu$-fractional derivative…

Let $\Pi$ be the fundamental group of a smooth variety X over $F_p$. Given a non-Archimedean place $\lambda$ of the field of algebraic numbers which is prime to p, consider the $\lambda$-adic pro-semisimple completion of $\Pi$ as an object…

The MolMod database is presented, which is openly accessible at http://molmod.boltzmann-zuse.de/ and contains presently intermolecular force fields for over 150 pure fluids. It was developed and is maintained by the Boltzmann-Zuse Society…

The Transformer architecture has dominated machine learning in a wide range of tasks. The specific characteristic of this architecture is an expensive scaled dot-product attention mechanism that models the inter-token interactions, which is…

In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…

Metal-organic frameworks (MOFs) are porous materials composed of metal ions and organic linkers. Due to their chemical diversity, MOFs can support a broad range of applications in chemical separations. However, the vast amount of structural…

We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an…

These notes are very informal notes on the Langlands program. I had some pleasure in daring to ask colleagues to explain to me the importance of some of the recent results on Langlands program, so I thought I will record (to the best of my…

Nowadays, scientific databases have become the bread-and-butter of particle physicists. These databases must be maintained and checked repeatedly to insure the accuracy of their content. The COMPETE collaboration aims at motivating data…

Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field -- assumed to be the real or the complex numbers -- and which contains the field. Notably, we consider Fueter…

This is a write-up for the plenary ICM talk, 2026. The goal of this paper is to propose a set of conjectures whose aim is to answer the basic question of the Langlands program (over function fields): how to describe the space of automorphic…

We give a proof of the existence of Asai, exterior square, and symmetric square local $L$-functions, $\gamma$-factors and root numbers in characteristic $p$, including the case of $p = 2$. Our study is made possible by developing the…

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…

We give a characterisation of the field into which quotients of values of L-functions associated to a cusp form belong. The construction involves shifted convolution series of divisor sums and to establish it we combine parts of F. Brown's…

Lennard-Jones (LJ) fluids serve as an important theoretical framework for understanding molecular interactions. Binary LJ fluids, where two distinct species of particles interact based on the LJ potential, exhibit rich phase behavior and…

The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules…

Large language models (LLMs) are advancing rapidly. Such models have demonstrated strong capabilities in learning from large-scale (unstructured) text data and answering user queries. Users do not need to be experts in structured query…