Related papers: Hidden sign in Langlands' correspondence
These notes cover background material on trees which are used in the paper `On uniqueness of the signature of a path of variation and the reduced path group'.
We study syllogistic reasoning in LLMs from the logical and natural language perspectives. In process, we explore fundamental reasoning capabilities of the LLMs and the direction this research is moving forward. To aid in our studies, we…
A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate…
Li\'enard-type equations are used for the description of various phenomena in physics and other fields of science. Here we find a new family of the Li\'enard-type equations which admits a non-standard autonomous Lagrangian. As a by-product…
This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the standard literature. Consequently,…
We present theoretical and numerical evidence for a random matrix theoretic approach to a conjecture about vanishings of quadratic twists of certain L-functions
The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain…
The Kerr/CFT correspondence provides a holographic description of spinning black holes that exist in our universe, and the notion of hidden conformal symmetry allows for a formulation of this correspondence away from extremality. In this…
It is our aim in this note to give a counter example to an argument used in the proof of the main theorem of the paper: On iterations for families of asymptotically pseudocontractive mappings, Applied Mathematics Letters, 24 (2011), 33-38…
In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic…
In this note, we answer a question on the extension of $L^{2}$ holomorphic functions posed by Ohsawa.
The success of pre-trained contextualized representations has prompted researchers to analyze them for the presence of linguistic information. Indeed, it is natural to assume that these pre-trained representations do encode some level of…
In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard…
Signed graphs have appeared in a broad variety of applications, ranging from social networks to biological networks, from distributed control and computation to power systems. In this paper, we investigate spectral properties of signed…
We develop Lie's correspondence and an explicit Baker-Campbell-Hausdorff formula for commutative automorphic formal loops.
These are expanded notes of some lectures given by the author for a workshop held at the Indian Statistical Institute, Bangalore in June, 2010, giving an exposition on the modular representations of finite groups of Lie type and $p$-adic…
We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance…
This article presents a general and flexible method for prompting a large language model (LLM) to reveal its (hidden) token input embedding up to homeomorphism. Moreover, this article provides strong theoretical justification -- a…
The Lewis Correspondence attaching a unique "period function" to each Maass wave form for SL(2,Z) is extended to subgroups of finite index. This is achieved by using vector-valued forms.
Given a (not necessarily regular) holonomic D-module defined on the product of two complex manifolds, we prove that the associated correspondence commutes (in some sense) with the De Rham functor. We apply this result to the study of the…