A sharpening of the bounds for linear forms in logarithms II
A sharpening of the bounds for linear forms in logarithms III
A sharper bound for the least pair of consecutive k-th power non-residues of non-principal characters (mod p) of order k > 3
A short intervals result for linear equations in two prime variables.
Given A and B integers relatively prime, we prove that almost all integers n in an interval of the form [N, N+H], where N exp(1/3+e) ≤ H ≤ N can be written as a sum Ap1 + Bp2 = n, with p1 and p2 primes and e an arbitrary positive constant. This generalizes the results of Perelli et al. (1985) established in the classical case A=B=1 (Goldbach's problem).
A short note on the difference between inverses of consecutive integers modulo .
A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences.
A short proof of a known density result.
A short proof of a series evaluation in terms of harmonic numbers.
A short proof of Fermat's two-square theorem given by János Bolyai.
A short proof of Rost nilpotence via refined correspondences.
A Siegel modular 3-fold that is a Picard modular 3-fold
A sieve approach to the Waring-Goldbach problem. I. Sums of four cubes
A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem
A simple construction of basic polynomials invariant under the Weyl group of the simple finite-dimensional complex Lie algebra
For every simple finite-dimensional complex Lie algebra, I give a simple construction of all (except for the Pfaffian) basic polynomials invariant under the Weyl group. The answer is given in terms of the two basic polynomials of smallest degree.
A simple construction of minimal asymptotic bases
A simple criterion for solvability of both and .
A simple proof of the mean fourth power estimate for and
A simple proof of the Ramanujan conjecture for powers of 5.
A simplification of the formula for L(1,χ) where χ is a totally imaginary Dirichlet character of a real quadratic field
A singular series average and Goldbach numbers in short intervals