The generalized Hardy-Littlewood's problem involving a quadratic polynomial with coprime discriminants
The hyperbola
We include several results providing bounds for an interval on the hyperbola containing lattice points.
The inner periodic structure of a function.
The k-tuple jumping champions among consecutive primes
The lattice points of an n-dimensional tetrahedron.
The lattice points of an n-dimensional tetrahedron. (Summary).
The localisation of primes in arithmetic progressions of irrational modulus
A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.
The moments of partitions, I
The moments of partitions, II
The monoid of ordered partitions of a natural number.
The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications
The paper is devoted to the derivation of the expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory. We provide a refinement based on a new property of -cores, and give an elementary proof by using the Macdonald identities. We also obtain an extension by adding two more parameters, which appears to be a discrete interpolation between the Macdonald identities and the generating function...
The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes
The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes (II)
The number of powers of 2 in a representation of large odd integers
The number of solutions of a homogeneous linear congruence
The number Γ(k) in Waring's problem
The number-theoretic content of the Jacobi triple product identity.
The overpartition function modulo 128.
The Piltz divisor problem in number fields: An improved lower bound by Soundararajan's method
The polynomial part of a restricted partition function related to the Frobenius problem.