Some problems concerning roots of polynomials with Dirichlet characters as coefficients
Some problems in multidimensional analytic number theory
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 involving powers of integers
Some problems of analytic number theory
Some problems of combinatorial number theory related to Bertrand's postulate.
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 problems on mean values of the Riemann zeta-function
Several problems and results on mean values of are discussed. These include mean values of and the fourth moment of for .
Some problems on splittings of groups.
Some product formulas for theta functions in one and two variables
Some properties of a certain nonaveraging sequence.
Some properties of Buck's measure density
Some properties of Fourier coefficients of Eisenstein series of degree two.
Some properties of orders of quaternion algebras with regard to the discrete norm
Quaternion algebras are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.
Some properties of the Euler quotient matrix.
Some properties of the multiple binomial transform and the Hankel transform of shifted sequences.