On polynomial Gauss sums (mod Pⁿ), n ≥ 2
On polynomial transformations in several variables
On polynomial-exponential equations.
On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II
On polynomials of the form .
On polynomials taking small values at integral arguments
On polynomials taking small values at integral arguments II
On polynomials that are sums of two cubes.
It is proved that, if F(x) be a cubic polynomial with integral coefficients having the property that F(n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F(x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F(n) is merely assumed to be a sum of two integral cubes of either sign. It is deduced that analogous propositions are true...
On polynomials that are sums of two perfect qth powers
On polynomials with flat squares
On Popov's explicit formula and the Davenport expansion
We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series we mean an infinite series involving a PNT (Prime Number Theorem) related to arithmetic function with the periodic Bernoulli polynomial weight and PNT arithmetic functions include the von Mangoldt function, Möbius function and Liouville function, etc. The Riesz sum of order or gives the well-known explicit formula for respectively the partial...
On positive definite Hermitian forms.
On positive definite quadratic polynomials
On positive integers with a certain nondivisibility property.
On power integral bases for certain pure number fields defined by
Let be a number field generated by a complex root of a monic irreducible polynomial , , is a square free rational integer. We prove that if or and , then the number field is monogenic. If or , then the number field is not monogenic.
On power residue characters of units and the representation of numbers by quadratic forms
On power residues
On power residues
On power series and Mahler's U-numbers.
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications