72 citations · 140 across the 39 of their papers we have counts for
12 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…
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…
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 <…
Sharp bounds for the number of rational points on algebraic curves and dimension growth, over all global fields
Gal Binyamini, Raf Cluckers, Fumiharu Kato
Let be an algebraic curve over a number field , and denote by the degree of over . We prove that the number of -rational poin…
Bounds for rational points on algebraic curves, optimal in the degree, and dimension growth
Gal Binyamini, Raf Cluckers, Dmitry Novikov
Bounding the number of rational points of height at most on irreducible algebraic plane curves of degree has been an intense topic of investigation since the work by Bombie…
An effective Pila-Wilkie theorem for sets definable using Pfaffian functions, with some diophantine applications
Gal Binyamini, Gareth O. Jones, Harry Schmidt +1
We prove an effective version of the Pila-Wilkie Theorem for sets definable using Pfaffian functions, providing effective estimates for the number of algebraic points of bounded he…
Rational points of rigid-analytic sets: a Pila-Wilkie type theorem
Gal Binyamini, Fumiharu Kato
We establish a rigid-analytic analog of the Pila-Wilkie counting theorem, giving sub-polynomial upper bounds for the number of rational points in the transcendental part of a $\mat…
Lower bounds for Galois orbits of special points on Shimura varieties: a point-counting approach
Gal Binyamini, Harry Schmidt, Andrei Yafaev
Let be a Shimura variety and let be a Weil height function on . We conjecture that the heights of special points in are discriminant negligible. Assuming this conjec…
Effective André-Oort for non-compact curves in Hilbert modular varieties
Gal Binyamini, David Masser
In the proofs of most cases of the André-Oort conjecture, there are two different steps whose effectivity is unclear: the use of generalizations of Brauer-Siegel and the use of Pil…
Density of algebraic points on Noetherian varieties
Gal Binyamini
Let be a relatively compact domain. A finite collection of real-valued functions on is called a \emph{Noetherian chain} if the partial derivatives of ea…
Multiplicity estimates, analytic cycles and Newton polytopes
Gal Binyamini
We consider the problem of estimating the multiplicity of a polynomial when restricted to the smooth analytic trajectory of a (possibly singular) polynomial vector field at a given…