Hypergeometric motives

DP Roberts, FR Villegas - Notices of the American Mathematical Society, 2022 - ams.org
… Watkins has written a very useful hypergeometric motive package [Wat15] in Magma and
throughout this article we indicate how to use it by including small snippets of Magma code …

[PDF][PDF] Hypergeometric motives

FR Villegas, H Cohen, T Dokchitser, K Kedlaya - Lecture notes, 2017 - heilbronn.ac.uk
… How are Hodge vectors distributed among all motives? … ► Katz’s hypergeometric trace …
► Our motive is a piece of the middle cohomology of …

On a certain hypergeometric motive of weight 2 and rank 3

B Naskrecki - arXiv preprint arXiv:1702.07738, 2017 - arxiv.org
… of hypergeometric motives H(α, β|t) attached to a pair of tuples α = (1/4, 1/2, 3/4), β = (0, 0, 0).
To each such motive … finite field analogue of complex hypergeometric function. Geometry of …

Special Hypergeometric Motives and Their L-Functions: Asai Recognition

L Dembélé, A Panchishkin, J Voight… - Experimental …, 2022 - Taylor & Francis
… In this paper, we illustrate some features of hypergeometric motives attached to particular
arithmetically significant hypergeometric identities for 1 / π and 1 / π 2 . To motivate this …

Hypergeometric motives and the generalized Fermat equation

FG Madriaga, A Pacetti - arXiv preprint arXiv:2412.08804, 2024 - arxiv.org
… The goal of the present article is to show how hypergeometric motives are more natural
objects to obtain the global representations constructed by Darmon, allowing to prove most steps …

Hypergeometric Motives from Euler Integral Representations

TL Kelly, J Voight - arXiv preprint arXiv:2412.03257, 2024 - arxiv.org
… ] already sees hypergeometric motives not defined over Q). Lastly… a nicer geometric realization
of hypergeometric motives that is … hypergeometric motives and Hecke Grossencharacters. …

Alternate Mirror Families and Hypergeometric Motives

CF Doran, TL Kelly, A Salerno, S Sperber, J Voight… - 2017 MATRIX …, 2019 - Springer
… Finally, we will discuss how all of this relates to hypergeometric motives. This report …
Picard–Fuchs equation is a hypergeometric differential equation whose motive descends to Q. For a …

[PDF][PDF] Periods and Motives: Applications in Mathematical Physics

D Li - 2012 - diginole.lib.fsu.edu
motives. In this work, we consider two problems in mathematical physics as applications of
the ideas and tools from periods and motives… generally given by hypergeometric functions. …

Lauricella hypergeometric functions, unipotent fundamental groups of the punctured Riemann sphere, and their motivic coactions

F Brown, C Dupont - Nagoya Mathematical Journal, 2023 - cambridge.org
… ‘motives’ associated with certain hypergeometric integrals, viewed as functions of their
parameters. It goes beyond the classical theory of motives, … ’s 2F1 hypergeometric function, which …

Transformations of hypergeometric motives

JW Hoffman, FT Tu - arXiv preprint arXiv:2003.05031, 2020 - arxiv.org
… In section 6 we give the definition of hypergeometric motives used in this paper. In 7 we prove
a theorem that allows one to deduce a transformation formula for ℓ-adic sheaves, knowing …