Evaluation of Some Convolution Sums and Representation Numbers of Quadratic Forms of Discriminant -135
Barış Kendirli *
Department of Mathematics, Faculty of Arts and Sciences, Fatih University, Buyukcekmece 34500 Istanbul, Turkey.
*Author to whom correspondence should be addressed.
Abstract
We evaluate the convolution sums
using the theory of quasimodular forms and determine the number of representations of a positive integer n by some direct sum of the forms
of discriminant -135 by
modular forms. Moreover, we explain how to determine the number of representations of Q + tP, t > 1, t|135 for various sums Q , P of the above quadratic forms.
Keywords: Quasimodular forms, divisor functions, convolution sums, representation number.