On a Diophantine inequality for forms of additive type
On a diophantine inequality involving prime numbers
On a Diophantine problem of Bennett
On a diophantine problem with one prime, two squares of primes and s powers of two
On a Diophantine problem with two primes and s powers of two
On a direct sum decomposition of the Dem'yanenko matrix
On a distribution problem in finite sets
On a divisibility problem
On a divisibility problem
Let be the sequence of all primes in ascending order. Using explicit estimates from the prime number theory, we show that if , then which improves a previous result of the second author.
On a divisor problem related to the Epstein zeta-function, IV
On a dynamical Brauer–Manin obstruction
Let be a morphism of a variety defined over a number field , let be a -subvariety, and let be the orbit of a point . We describe a local-global principle for the intersection . This principle may be viewed as a dynamical analog of the Brauer–Manin obstruction. We show that the rational points of are Brauer–Manin unobstructed for power maps on in two cases: (1) is a translate of a torus. (2) is a line and has a preperiodic coordinate. A key tool in the proofs is the classical...
On a family of cubic Thue equations with 5 solutions
On a family of elliptic curves.
On a family of elliptic curves of rank at least 2
Let be a family of elliptic curves over , where is a positive integer and , are distinct odd primes. We study the torsion part and the rank of . More specifically, we prove that the torsion subgroup of is trivial and the -rank of this family is at least 2, whenever , and with neither nor dividing .
On a family of generalized Pascal triangles defined by exponential Riordan arrays.
On a Fermat Equation Arising in the Arithmetic Theory of Function Fields.
On a few Diophantine equations, in particular, Fermat's Last Theorem.
On a form of the Erdős-Turán inequality
On a function related to Ramanujan's tau function.
On a functional equation satisfied by certain Dirichlet series