Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Jonathan Pila"'
Autor:
Jonathan Pila, Jacob Tsimerman
Publikováno v:
Journal of the European Mathematical Society. 24:3161-3182
We prove a result which describes, for each $n\ge 1$, all linear dependencies among $n$ images in elliptic curves of special points in modular or Shimura curves under parameterizations (or correspondences). Our result unifies and improves in certain
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::112bd2a86167ac957e7635b6001d268c
https://doi.org/10.4171/jems/1161
https://doi.org/10.4171/jems/1161
Autor:
Jonathan Pila
Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink conjectures. The results combine ideas close to transcendence the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ffa6b44bd9b25cd072f264861f895a6f
https://doi.org/10.1017/9781009170314
https://doi.org/10.1017/9781009170314
Publikováno v:
Annals of Mathematics. 189
We prove the Ax-Schanuel theorem for a general (pure) Shimura variety. A basic version of the theorem concerns the transcendence of the uniformization map from a bounded Hermitian symmetric space to a Shimura variety. We then prove a version of the t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cec630e6be18db6660c5356513a4ea6b
https://doi.org/10.4007/annals.2019.189.3.7
https://doi.org/10.4007/annals.2019.189.3.7
Autor:
Jacob Tsimerman, Jonathan Pila
Publikováno v:
Annals of Mathematics. 179:659-681
We prove the Ax-Lindemann theorem for the coarse moduli space A g of principally polarized abelian varieties of dimension g=1 . We affirm the Andre-Oort conjecture unconditionally for A g for g=6 , and under GRH for all g
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https://explore.openaire.eu/search/publication?articleId=doi_________::c0ba3b8d399c71e2108b1eaa970b763e
https://doi.org/10.4007/annals.2014.179.2.5
https://doi.org/10.4007/annals.2014.179.2.5
Autor:
Jonathan Pila
Publikováno v:
Mathematika. 60:1-31
We prove a special point result for products of elliptic modular surfaces, elliptic curves, multiplicative groups and complex lines, and deduce a result about vanishing linear combinations of singular moduli and roots of unity. © University College
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::625dce8c304ae9b56cf33f9fa0377d66
https://doi.org/10.1112/s0025579313000168
https://doi.org/10.1112/s0025579313000168
Autor:
Jonathan Pila
We consider some diophantine problems suggested by the analogy between multiplicative groups and powers of the modular curve in problems of "unlikely intersections." We prove a special case of the Zilber-Pink conjecture for curves.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f65688e98987d9ad2510ba3f84030612
Publikováno v:
Proc. London Mathematical Soc., 84(3), 2361-2401
This series of papers presents and rigorously analyzes a probabilistic algorithm for finding small prime factors of an integer. The algorithm uses the Jacobian varieties of curves of genus 2 in the same way that the elliptic curve method uses ellipti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::16da386ce09b7e947e36bd6d33525061
https://doi.org/10.1112/plms/84.1.105
https://doi.org/10.1112/plms/84.1.105
Autor:
Jonathan Pila
We prove some simple special cases, partly new, of results of André-Oort-Manin-Mumford type using an extension to algebraic points of bounded degree of a result of Pila-Wilkie on the density of rational points on sets definable in an o-minimal struc
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10dcb38d36d10416d41195d1b2c99942
https://doi.org/10.1093/imrn/rnp022
https://doi.org/10.1093/imrn/rnp022
Autor:
Jonathan Pila
Let f be an entire function that is real and strictly increasing for all sufficiently large real arguments, and that satisfies certain additional conditions, and let Xf be the set of non-negative real numbers at which f is integer valued. Suppose g i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ec34c99e7e9143504bfbbbdc1495654
https://ora.ox.ac.uk/objects/uuid:44be83f8-758c-4a6c-be2c-5424688ddaef
https://ora.ox.ac.uk/objects/uuid:44be83f8-758c-4a6c-be2c-5424688ddaef
Autor:
Jonathan Pila
A classic theorem of Pólya shows that 2z is, in a strong sense, the "smallest" transcendental entire function that is integer valued on ℕ. An analogous result of Gel'fond concerns entire functions that are integer valued on the set Xa = {an: n ∈
Externí odkaz:
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https://ora.ox.ac.uk/objects/uuid:44cfd2d2-b003-499d-968f-f4710560e972
https://ora.ox.ac.uk/objects/uuid:44cfd2d2-b003-499d-968f-f4710560e972