Some congruences for the partial Bell polynomials.
Some formulas that enumerate certain partitions and graphs
Some general problems on the number of parts in partitions
Some identities involving the partition function
Some mean-value theorems for exponential sums
Some new estimates for G(k) in Waring's problem
Some new infinite families of congruences modulo 3 for overpartitions into odd parts
Let denote the number of overpartitions of n in which only odd parts are used. Some congruences modulo 3 and powers of 2 for the function have been derived by Hirschhorn and Sellers, and Lovejoy and Osburn. In this paper, employing 2-dissections of certain quotients of theta functions due to Ramanujan, we prove some new infinite families of Ramanujan-type congruences for modulo 3. For example, we prove that for n, α ≥ 0, .
Some partition problems related to the Stirling numbers of the second kind
Some problems about the ternary quadratic form m₁² + m₂² + m₃²
Some problems in number theory, combinatorics and combinatorial geometry.
Some problems in number theory that arise from group theory.
In this expository paper, we present several open problerns in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Some problems of 'Partitio numerorum'; I: A new solution of Waring`s problem
Some Problems of "Partitio numerorum": II Proof that every large number is the sum of at most 21 biquadrates
Some problems of "Partitio Numerorum": IV The singular series in Waring's Problem and the value of the number G (k)
Some problems of Waring?s type
Some Recent Developments in three Classical Problems of Number Theory.
Some remarks on Goldbach's problem
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