Mean values of dedekind sums

The aim of this thesis is to obtain some identities and recursion relations concerning Bernoulli, Euler, Genocchi polynomials and numbers; to find generators which give the entries of Euler-Seidel matrices and to determine the types of Euler-Seidel matrices. Firstly, Dedekind sums, Stirling numbers, Bernoulli, Euler, Genocchi polynomials and numbers are defined; fundemental properties of these sums, numbers and polynomials are given also identities and recursion relations of these polynomials, numbers are investigated. Besides, The Akiyama-Tanigawa algorithm for these numbers is given. Then Euler-Seidel matrices are defined, some of their properties are given and with some examples the subject is studied in detail. Furthermore the connection between Euler-Seidel matrices and Bernoulli, Euler, Genocchi and Tangent numbers is established. In the final section it is proved that the type of Euler-Seidel matrices on Z_{p} is p(p-1)×p. New generators for a_{n}^{k} which are entries of Euler-Seidel matrices are obtained. Also relations for Genocchi polynomials and numbers are obtained in a similar fashion to the relations for Bernoulli and Euler polynomials and numbers given bye Sun, Pan, Wu (2004).