Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Alexandru Buium"'
Autor:
Alexandru Buium, Lance Edward Miller
A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed p-adic fields. As an app
Autor:
Alexandru Buium, Emma Previato
Publikováno v:
Journal of Number Theory
In this note, we prove a finiteness result for fibers that are canonical lifts in a given elliptic fibration. The question was motivated by the authors' construction of an arithmetic Euler top, and it highlights an interesting discrepancy between the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ddf8f6236cfd4053475b30816bf49786
https://doi.org/10.1016/j.jnt.2018.02.008
https://doi.org/10.1016/j.jnt.2018.02.008
Autor:
Alexandru Buium, Emma Previato
Publikováno v:
Journal of Number Theory. 173:37-63
The theory of differential equations has an arithmetic analogue in which derivatives of functions are replaced by Fermat quotients of numbers. Many classical differential equations (Riccati, Weierstrass, Painleve, etc.) were previously shown to posse
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::69b879d7ea2d480f7f3efc851296d31a
https://doi.org/10.1016/j.jnt.2016.09.024
https://doi.org/10.1016/j.jnt.2016.09.024
Autor:
Alexandru Buium, Lance Edward Miller
Publikováno v:
Advances in Mathematics
Arithmetic differential equations or δ-geometry exploits analogies between derivations and p-derivations δ arising from lifts of Frobenius to study problems in arithmetic geometry. Along the way, two main classes such functions, describable as seri
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::31404ae82899eab14389edba2dd189cc
Autor:
Alexandru Buium
Publikováno v:
Selecta Mathematica
This paper is part of a series of papers where an arithmetic analogue of classical differential geometry is being developed. In this arithmetic differential geometry functions are replaced by integer numbers, derivations are replaced by Fermat quotie
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e005687fa4c9ec19cc8fe482cb40690f
https://hdl.handle.net/21.11116/0000-0004-7546-A21.11116/0000-0004-7548-821.11116/0000-0004-7549-7
https://hdl.handle.net/21.11116/0000-0004-7546-A21.11116/0000-0004-7548-821.11116/0000-0004-7549-7
Autor:
Alexandru Buium, Taylor Dupuy
Publikováno v:
Journal of Algebra. 454:273-291
The theory of differential equations has an arithmetic analogue [8] in which derivatives are replaced by Fermat quotients. One can then ask what is the arithmetic analogue of a linear differential equation. The study of usual linear differential equa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a0e62fd5b16bebde7329595bf9b40d73
https://doi.org/10.1016/j.jalgebra.2016.01.026
https://doi.org/10.1016/j.jalgebra.2016.01.026
Autor:
Alexandru Buium, Taylor Dupuy
Publikováno v:
Selecta Mathematica. 22:529-552
Differential equations have arithmetic analogues (Buium in Arithmetic differential equations, Mathematical Surveys and Monographs, vol 118. American Mathematical Society, Providence 2005) in which derivatives are replaced by Fermat quotients; these a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ba7526ae3a6e9b076e737cea2acbf982
https://doi.org/10.1007/s00029-015-0197-7
https://doi.org/10.1007/s00029-015-0197-7
Autor:
Alexandru Buium, Taylor Dupuy
Publikováno v:
Selecta Mathematica. 22:447-528
Motivated by the search of a concept of linearity in the theory of arithmetic differential equations (Buium in Arithmetic differential equations. Math. surveys and monographs, vol 118. American Mathematical Society, Providence, 2005), we introduce he
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::07c7fcba22a1715053faae441e9db8b7
https://doi.org/10.1007/s00029-015-0194-x
https://doi.org/10.1007/s00029-015-0194-x
Autor:
Alexandru Buium
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate fu