5 citations · 14 across the 11 of their papers we have counts for
9 papers · 1 filter
On linear independence of Dirichlet values
Sanoli Gun, Neelam Kandhil, Patrice Philippon
The study of linear independence of for a fixed integer and varying depends critically on the parity of vis-à-vis . This has been investigated by a numbe…
Semi-abelian analogues of Schanuel Conjecture and applications
Cristiana Bertolin, Patrice Philippon, Biswajyoti Saha +1
In this article we study Semi-abelian analogues of Schanuel conjecture. As showed by the first author, Schanuel Conjecture is equivalent to the Generalized Period Conjecture applie…
On two problems of Hardy and Mahler
Patrice Philippon, Purusottam Rath
It is a classical result of Mahler that for any rational number > 1 which is not an integer and any real 0 < c < 1, the set of positive integers n such that n < c n is nece…
An abelian analogue of Schanuel's conjecture and applications
Patrice Philippon, Biswajyoti Saha, Ekata Saha
In this article we study an abelian analogue of Schanuel's conjecture. This conjecture falls in the realm of the generalised period conjecture of Y. Andr{é}. As shown by C. Bertoli…
The distribution of Galois orbits of points of small height in toric varieties
José Ignacio Burgos Gil, Patrice Philippon, Juan Rivera-Letelier +1
We address the distribution properties of points of small height on proper toric varieties and applications to the related Bogomolov property. We introduce the notion of monocritic…
Height of varieties over finitely generated fields
Jose Ignacio Burgos Gil, Patrice Philippon, Martin Sombra
We show that the height of a variety over a finitely generated field of characteristic zero can be written as an integral of local heights over the set of places of the field. This…
Successive minima of toric height functions
Jose Ignacio Burgos Gil, Patrice Philippon, Martin Sombra
Given a toric metrized R-divisor on a toric variety over a global field, we give a formula for the essential minimum of the associated height function. Under suitable positivity co…
Essential minimum and obstruction degrees of translates of subtori
Patrice Philippon, Martin Sombra
We study the obstruction degrees of translates of sub-tori of multiplicative tori and we show how they are connected to lower bounds for the essential minimum of these varieties. I…
Normalized height of projective toric varieties
Patrice Philippon, Martin Sombra
We present an explicit expression for the normalized height of a projective toric variety. This expression decomposes as a sum of local contributions, each term being the integral…