Zobrazeno 1 - 10
of 70
pro vyhledávání: '"Aslanyan, Vahagn A."'
Autor:
Aslanyan, Vahagn
We explore systems of polynomial equations where we seek complex solutions with absolute value 1. Geometrically, this amounts to understanding intersections of algebraic varieties with tori -- Cartesian powers of the unit circle. We study the propert
Externí odkaz:
http://arxiv.org/abs/2409.12867
Autor:
Aslanyan, Vahagn, Gallinaro, Francesco
This is an expository paper aiming to introduce Zilber's Exponential Closedness conjecture to a general audience. Exponential Closedness predicts when (systems of) equations involving addition, multiplication, and exponentiation have solutions in the
Externí odkaz:
http://arxiv.org/abs/2409.12860
Autor:
Aslanyan, Vahagn, Kirby, Jonathan
We characterise the model-theoretic algebraic closure in Zilber's exponential field. A key step involves showing that certain algebraic varieties have finite intersections with certain finite-rank subgroups of the graph of exponentiation. Mordell-Lan
Externí odkaz:
http://arxiv.org/abs/2405.01399
Autor:
Aslanyan, Vahagn
This paper aims to give a brief account of the mathematical work of the 7th-century Armenian polymath and natural philosopher Anania Shirakatsi. The three sections of Anania's ``Book of Arithmetic'' -- tables of arithmetic operations, a list of probl
Externí odkaz:
http://arxiv.org/abs/2404.15945
Autor:
Aslanyan, Vahagn
In this paper we survey the history of, and recent developments on, two major conjectures originating in Zilber's model-theoretic work on complex exponentiation -- Existential Closedness and Zilber-Pink. The main focus is on the modular versions of t
Externí odkaz:
http://arxiv.org/abs/2403.09304
We show that for any polynomial $F(X,Y_0,Y_1,Y_2) \in \mathbb{C}[X, Y_0, Y_1, Y_2]$, the equation $F(z,j(z),j'(z),j''(z))=0$ has a Zariski dense set of solutions in the hypersurface $F(X,Y_0,Y_1,Y_2)=0$, unless $F$ is in $\mathbb{C}[X]$ or it is divi
Externí odkaz:
http://arxiv.org/abs/2312.09974
Let $n \in \mathbb{Z}_{>0}$. We prove that there exist a finite set $V$ and finitely many algebraic curves $T_1, \ldots, T_k$ with the following property: if $(x_1, \ldots, x_n, y)$ is an $(n+1)$-tuple of pairwise distinct singular moduli such that $
Externí odkaz:
http://arxiv.org/abs/2308.12244
Publikováno v:
Annals of Pure and Applied Logic (2023), 103288
We give four different independence relations on any exponential field. Each is a canonical independence relation on a suitable Abstract Elementary Class of exponential fields, showing that two of these are NSOP$_1$-like and non-simple, a third is st
Externí odkaz:
http://arxiv.org/abs/2211.03071
Autor:
Aslanyan, Vahagn, Daw, Christopher
We discuss the relationships between the Andr\'e-Oort, Andr\'e-Pink-Zannier, and Mordell-Lang conjectures for Shimura varieties. We then combine the latter with the geometric Zilber-Pink conjecture to obtain some new results on unlikely intersections
Externí odkaz:
http://arxiv.org/abs/2209.07967
Autor:
Aslanyan, Vahagn, Daw, Christopher
Publikováno v:
In Journal of Number Theory July 2024 260:212-222
