Higher-order character Dedekind sum

Higher Dimensional Dedekind Sums

In this paper we will study the number-theoretical properties of the expression v1 nkal rcka,, d(p; a I . . . . . an) = ( 1) n/2 ~ cot cot (1) k=l P P and of related finite trigonometric sums. In Eq. (I), p is a positive integer, a~ . . . . . a, are integers prime to p, and n is even (for n odd the sum is clearly equal to zero). There are two reasons for being interested in sums of this type. F...

Some Higher Order Triangular Sum Labeling of Graphs

A (p,q) graph G is said to admit n order triangular sum labeling if its vertices can be labeled by non negative integers such that the induced edge labels obtained by the sum of the labels of end vertices are the first q n order triangular numbers. A graph G which admits n order triangular sum labeling is called n order triangular sum graph. In this paper we prove that paths, combs, stars, subd...

The Friedlander–iwaniec Character Sum

As we observed in [3], one can also interpret the sums S(α;β) as special cases of the correlation sums arising in our work on algebraic twists of modular forms, and we also noted that our more general results and techniques had, as special case, this theorem of Birch and Bombieri. Very recently, Y. Zhang [12, Lemma 12] made a crucial use of this estimate in his work on bounded gaps between prim...

On a Sum Analogous to Dedekind Sum and Its Mean Square Value Formula

Fourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...