Title: A MODULAR FORMS APPROACH TO ARITHMETIC CONVOLUTED IDENTITIES

Link to Master’s project

Abstract.
In 2004, H. Farkas found a series of identities which relate the convolution of a certain arithmetic function with an analogue of the classical σ-function. In 2009, P. Guerzhoy and W. Raji interpreted series of identities of this kind using generating functions and modular forms. Their results pertain to primes p ≡ 3 mod 4. In this paper, we address the primes p ≡ 5 mod 8 and obtain four new series of similar identities. Our methods are close to those employed by Guerzhoy and Raji.