EVALUATION OF THE CONVOLUTION SUM Sigma(al+bm=n) sigma(l)sigma(m) FOR (a, b) = (1, 48), (3, 16), (1, 54), (2, 27)

WOS: 000487845900002We determine the convolution sum Sigma(al+bm=n) sigma(l)sigma(m) for (a, b) = (1, 48), (3, 16), (1, 54), (2, 27) for all positive integers n. We then use these evaluations together with known evaluations of other convolution sums to determine the numbers of representations of n by the octonary quadratic forms k(x(1)(2) +x(1)x(2) + x(2)(2) + x(3)(2)+ x(3)x(4) + x(4)(2)) + l(x(5)(2) + x(5)x(6) + x(6)(2) + x(7)(2) + x(7)x(8) + x(8)(2)) for (k, l) = (1, 16), (1, 18), (2, 9). A modular form approach is used.Scientific and Technological Research Council of Turkey (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK)The research was carried out during the first author's visit to Recep Tayyip Erdogan University, Rize, Turkey. He would like to thank Recep Tayyip Erdogan University for the hospitality during his stay. He also thanks the Scientific and Technological Research Council of Turkey (TUBITAK) for the financial support

On Suborbital Graphs for the Group Gamma(3)

WOS: 000515992900002In this paper, we investigate suborbital graphs generated by the action of the group G 3 which is the group obtained from the third powers of the elements of the modular group G on Q. {8}. First, we give necessary and sufficient conditions for an edge to be in the related graphs. Then, we investigate connectedness of the graphs

Suborbital graphs for the group Gamma(2)

Guler, Bahadir Ozgur/0000-0003-3131-3643; Deger, Ali Hikmet H/0000-0003-0764-715X;WOS: 000368502000004In this paper, we investigate suborbital graphs formed by the action of 2 which is the group generated by the second powers of the elements of the modular group Gamma on (Q) over cap Q. Firstly, conditions for being an edge, self-paired and paired graphs are provided, then we give necessary and sufficient conditions for the suborbital graphs to contain a circuit and to be a forest. Finally, we examine the connectivity of the subgraph F-u,(N) and show that it is connected if and only if N <= 2