Lethbridge Number Theory and Combinatorics Seminar: Selcuk Aygin

We use properties of modular forms to extend the Ramanujan-Mordell formula. Our result yields to formulas for representation numbers by the quadratic form ∑2ai=1x2i+∑2bi=1py2i, for all non-negative integers a,b and for all odd prime p. We obtain this result by computing the Fourier series expansions of modular forms at all cusps of Γ0(4p).