Relations binaires entre partitions
Remarks on some new applications of the dispersion method
Remarks on the paper "Sur certaines hypothèses concernant les nombres premiers"
Remarque à l'article precedent de M. Mahler
Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids.
Representation of odd integers as the sum of one prime, two squares of primes and powers of 2
Representation of odd integers as the sum of one prime, two squares of primes and powers of 2
Représentations comme sommes de carrés
Représentations des groupes et identités polynomiales
Plusieurs problèmes liés au problème de Waring utilisent des identités où l’on exprime une forme linéaire en comme somme ou différence de puissances -ièmes de formes linéaires en . La plupart de ces identités sont fournies par des solutions au problème de Tarry-Escott, sauf deux d’entre elles, dues à Rao et Vaserstein. Nous montrons que ces deux identités sont naturellement liées aux groupes et , puis développons une théorie qui permet d’associer à chaque groupe fini quelques identités de...
Representations of integers as sums of primes from a Beatty sequence
Restricted partitions.
Restricted set addition in Abelian groups: results and conjectures
We present a system of interrelated conjectures which can be considered as restricted addition counterparts of classical theorems due to Kneser, Kemperman, and Scherk. Connections with the theorem of Cauchy-Davenport, conjecture of Erdős-Heilbronn, and polynomial method of Alon-Nathanson-Ruzsa are discussed.The paper assumes no expertise from the reader and can serve as an introduction to the subject.
Restriction theory of the Selberg sieve, with applications
The Selberg sieve provides majorants for certain arithmetic sequences, such as the primes and the twin primes. We prove an – restriction theorem for majorants of this type. An immediate application is to the estimation of exponential sums over prime -tuples. Let and be positive integers. Write , where is the set of all such that the numbers are all prime. We obtain upper bounds for , , which are (conditionally on the Hardy-Littlewood prime tuple conjecture) of the correct order...
Résultats et problèmes en théorie des nombres
Rogers-Ramanujan identities: A century of progress from mathematics to physics.
Rogers-Ramanujan-Slater type identities.
Roth's theorem on systems of linear forms in function fields
Schur's determinants and partition theorems.
Self-conjugate vector partitions and the parity of the spt-function
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author,...
Semisemiological structure of the prime numbers and conditional Goldbach theorems.