Semisemiological structure of the prime numbers and conditional Goldbach theorems.
Structures related to Pascal’s triangle modulo and their elementary theories
The cyclicity problem for the images of Q-rational series
We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q.
The cyclicity problem for the images of Q-rational series
We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q.
The minimal resultant locus
Let K be a complete, algebraically closed nonarchimedean valued field, and let φ(z) ∈ K(z) have degree d ≥ 2. We study how the resultant of φ varies under changes of coordinates. For γ ∈ GL₂(K), we show that the map factors through a function on the Berkovich projective line, which is piecewise affine and convex up. The minimal resultant is achieved either at a single point in , or on a segment, and the minimal resultant locus is contained in the tree in spanned by the fixed points and poles...
The nonabsolute boundedness model of the theory of semisets
The positivity problem for fourth order linear recurrence sequences is decidable
The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.
The real field with the rational points of an elliptic curve
We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets definable in that structure are semialgebraic.
Twin prime problem in an arithmetic without induction
Ultraprodukte endlicher Körper.
Uniform p-adic cell decomposition and local zeta functions.
Арифметические представления степеней
Бесконечные множества простых чисел, допускающие диофантовы представления с восемью переменными
Диoфантово представление совершенных чисел
Некоторые вопросы полноты арифметики
Новая техника для получения диафантовых представлений путем устранения ограниченных кванторов общности
Новое доказательство теоремы об экспоненциально диофантовом представлении перечислимых предикатов
О разрешимости некоторых теорий целых чисел.
Относительно стандартные элементы в теории внутренних множеств Е.Нельсона.
Простые числа перечисляются полиномом от 10 переменных