Some Remarks on Vinogradov's Mean Value Theorem and Tarry's Problem.
Some results in additive number theory I: The critical pair theory
Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions
This paper generalizes some results from another one, namely [3]. We have studied the issues of expressing natural numbers as a sum of powers of natural numbers in paper [3]. It means we have studied sets of type where were given natural numbers. Now we are going to study a more general case, i.e. sets of natural numbers that are expressed as sum of integral parts of functional values of some special functions. It means that we are interested in sets of natural numbers in the form
Some theorems concerning the theory of primes.
Sommes de carrés
Sommes de carrés dans [Book]
Sommes de carrés de polynômes irréductibles dans
Sommes de carrés et d’irréductibles dans
Sommes de carrés, fonctions L et formes modulaires.
Sommes de cubes dans l’anneau
Sommes de deux carrés qui ne sont pas sommes de trois carrés strictement positifs
Sommes de diviseurs et structure multiplicative des entiers
Sommes de puissances d-ièmes dans un anneau commutatif
Sommes de puissances et d’irréductibles dans
Sommes des carrés et d’irréductibles dans
Sommes d’exponentielles dans
Sparsity of the intersection of polynomial images of an interval
We show that the intersection of the images of two polynomial maps on a given interval is sparse. More precisely, we prove the following. Let be polynomials of degrees d and e with d ≥ e ≥ 2. Suppose M ∈ ℤ satisfies , where E = e(e+1)/2 and κ = (1/d - 1/d²) (E-1)/E + ε. Assume f(x)-g(y) is absolutely irreducible. Then .
Special values of the dilogarithm function
Spectral factorization of trigonometric polynomials and lattice geometry
Srinivasa Ramanujan (1887-1920) and the theory of partitions of numbers and statistical mechanics. A centennial tribute.