Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Eterović, Sebastian"'
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
Autor:
Eterović, Sebastian, Padgett, Adele
Let $V\subseteq\mathbb{C}^{2n}$ be an algebraic variety with no constant coordinates and with a dominant projection onto the first $n$ coordinates. We show that the intersection of $V$ with the graph of the $\Gamma$ function is Zariski dense in $V$.<
Externí odkaz:
http://arxiv.org/abs/2310.01658
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
Autor:
Eterović, Sebastian, Scanlon, Thomas
We prove a general likely intersections theorem, a counterpart to the Zilber-Pink conjectures, under the assumption that the Ax-Schanuel property and some mild additional conditions are known to hold for a given category of complex quotient spaces de
Externí odkaz:
http://arxiv.org/abs/2211.10592
Autor:
Broudy, Isaac A., Eterović, Sebastian
Given a subfield $F$ of $\mathbb{C}$, we study the linear disjointess of the field $E$ generated by iterated exponentials of elements of $\overline{F}$, and the field $L$ generated by iterated logarithms, in the presence of Schanuel's conjecture. We
Externí odkaz:
http://arxiv.org/abs/2211.09556
Autor:
Eterović, Sebastian
Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular $j$ function can be reduced to the problem of finding a
Externí odkaz:
http://arxiv.org/abs/2209.12192
Autor:
Eterović, Sebastian, Zhao, Roy
Let $(G, X)$ be a Shimura datum, let $\Omega$ be a connected component of $X$, let $\Gamma$ be a congruence subgroup of $G(\mathbb{Q})^{+}$, and consider the quotient map $q: \Omega \to S:=\Gamma \backslash \Omega$. Consider the Harish-Chandra embedd
Externí odkaz:
http://arxiv.org/abs/2107.10392
Publikováno v:
Israel Journal of Mathematics, 2022
We prove some unconditional cases of the Existential Closedness problem for the modular $j$-function. For this, we show that for any finitely generated field we can find a "convenient" set of generators. This is done by showing that in any field equi
Externí odkaz:
http://arxiv.org/abs/2010.00102
Publikováno v:
Proc. Amer. Math. Soc. 149 (2021), 1417-1429
We prove the Existential Closedness conjecture for the differential equation of the $j$-function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the $j$-function have solut
Externí odkaz:
http://arxiv.org/abs/2003.10996
Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in which the
Externí odkaz:
http://arxiv.org/abs/1907.09858