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10 papers · 1 filter
A Structure Theory for Small Sum Subsets
Yahya Ould Hamidoune
We develop a new method leading the structure of finite subsets S and T of an abelian group with . We show also how to recover the known results in this area in a…
Solving Fermat-type equations x^5+y^5=dz^p
Nicolas Billerey, Luis Dieulefait
In this paper we are interested in solving the Fermat-type equations x^5+y^5=dz^p where d is a positive integer and p a prime number . We describe a new method based on modu…
Deformation data, Belyi maps, and the local lifting problem
Irene I. Bouw, Stefan Wewers, Leonardo Zapponi
We prove existence and nonexistence results for certain differential forms in positive characteristic, called {\em good deformation data}. Some of these results are obtained by red…
On complete subsets of the cyclic group
Y. O. Hamidoune, A. S. Lladó, O. Serra
A subset of an abelian is said to be {\em complete} if every element of the subgroup generated by can be expressed as a nonempty sum of distinct elements from . Let…
Rank One Solvable p-adic Differential Equation and Finite Abelian Characters via Lubin-Tate groups
Andrea Pulita
We introduce a new class of exponentials of Artin-Hasse type, called -exponentials. These exponentials depends on the choice of a generator of the Tate…
On the critical pair theory in Z/pZ
Yahya Ould Hamidoune, Oriol Serra, Gilles Zemor
Let A and B be subsets of Z/pZ such that |A+B| < |A|+|B|+2. We prove that, if |A|>3, |B|>4, |A+B|<p-4 and p > 52, then A and B are included in arithmetic progressions with the same…