6 papers · 1 filter
Asymptotic formulas for sums of elements from a multiplicative group
Jan-Hendrik Evertse, Kálmán Győry, Lajos Hajdu +2
Let be a number field, an integer, the -fold direct product of with coordinatewise multiplication, and a finitely generated subgroup of rank $r…
Effective reduction theory of integral polynomials of given non-zero discriminant and its applications
Jan-Hendrik Evertse, Kálmán Győry
We give a survey on the general effective reduction theory of integral polynomials and its applications. We concentrate on results providing the finiteness for the number of `$\mat…
On additive and multiplicative decompositions of sets of integers with restricted prime factors, I. (Smooth numbers.)
K. Győry, L. Hajdu, A. Sárközy
In [10] the third author of this paper presented two conjectures on the additive decomposability of the sequence of ''smooth'' (or ''friable'') numbers. Elsholtz and Harper [4] pro…
Number systems over general orders
Jan-Hendrik Evertse, Kálmán Győry, Attila Pethő +1
Let be an order, that is a commutative ring with whose additive structure is a free -module of finite rank. A generalized number system (GNS for short…
On the smallest number of terms of vanishing sums of units in number fields
Csanád Bertók, Kálmán Győry, Lajos Hajdu +1
Let be a number field. In the terminology of Nagell a unit of is called {\it exceptional} if is also a unit. The existence of such a unit is e…
Multiply monogenic orders
Attila Bérczes, Jan-Hendrik Evertse, Kálmán Győry
Let O be an order in an algebraic number field K, i.e., a ring with quotient field K which is contained in the ring of integers of K. The order O is called monogenic, if it is of t…