72 citations · 140 across the 39 of their papers we have counts for
9 papers · 1 filter
Ax-Schanuel for the Drinfeld -function
Gal Binyamini, Dmitry Novikov, Francesco Maria Saettone
We prove an analog of the Ax-Schanuel theorem for the Drinfeld -function in odd characteristic. Roughly speaking, if the graph of $\boldsymbol{j}\colonΩ^n\rightarrow\mathbb{A}^n…
Sharp zero estimates for trajectories of polynomial vector fields
Gal Binyamini, Yuval Salant
If is a tuple of functions satisfying an algebraic ODE and , it is common in applications to transcendental number theory to consider upper bounds for th…
Establishing the Polynomial Wolff Axioms for -Separated -Tubes With #o-minimality
Gal Binyamini, Yuval Salant
We establish the full version of a conjecture of Guth and Zahl, giving a lower bound for the volume of a semialgebraic set that has a large intersection with a collection of -se…
Logarithmic--exponential preparation in sharply o-minimal structures
Gal Binyamini, Oded Carmon, Dmitry Novikov
We develop a complex-analytic approach to the model theory of the (real) unrestricted exponential. As a consequence we derive sharp forms of many of the foundational results for th…
Estimating the number of real zeros of linear combinations of radicals of polynomials
Gal Binyamini, Avner Kiro, Alexander Logunov +2
We obtain upper bounds for the number of real zeros of functions of the form where and each $P_k…
The Pila-Zannier strategy for Drinfeld modules and Drinfeld modular curves
Gal Binyamini, Dmitry Novikov, Francesco Maria Saettone
We extend the Pila-Zannier strategy to Drinfeld modules: we prove analogues of the Manin-Mumford theorem for a product of two Drinfeld modules of equal rank, and of the André-Oort…
Algebraic Hodge generic points are dense
Gregorio Baldi, Gal Binyamini, David Urbanik
Let be a quasi-projective family of varieties defined over . We show that the points of that are H…
Counting Theorems for Algebraic Relations
Gal Binyamini, Noriko Hirata-Kohno, Makoto Kawashima +1
Let X be a set definable in a sharply o-minimal structure. We consider the problem of counting the number of points where X intersects algebraic varieties V over Q of dimension k <…
Complex cells in sharply o-minimal structures
Gal Binyamini, Oded Carmon, Dmitry Novikov
We extend the theory of complex cells introduced by Binyamini and Novikov to the sharply o-minimal setting, obtaining cellular preparation and parameterization theorems which are p…