Upper bounds on a two-term exponential sum*

2001 ◽  
Vol 44 (8) ◽  
pp. 1003-1015 ◽  
Author(s):  
Todd Cochrane ◽  
Zhiyong Zheng
Keyword(s):  
Exponential Sum ◽  
Upper Bounds

scholarly journals Resonance between the Representation Function and Exponential Functions over Arithemetic Progression

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Li Ma ◽  
Xiaofei Yan
Keyword(s):  
Positive Integer ◽  
Exponential Sum ◽  
Upper Bounds ◽  
Arithmetic Progressions ◽  
Large Parameter ◽  
Exponential Functions ◽  
Representation Function

Let r n denote the number of representations of a positive integer n as a sum of two squares, i.e., n = x 1 2 + x 2 2 , where x 1 and x 2 are integers. We study the behavior of the exponential sum twisted by r n over the arithmetic progressions ∑ n ∼ X n ≡ l mod q r n e α n β , where 0 ≠ α ∈ ℝ , 0 < β < 1 , e x = e 2 π i x , and n ∼ X means X < n ≤ 2 X . Here, X > 1 is a large parameter, 1 ≤ l ≤ q are integers, and l , q = 1 . We obtain the upper bounds in different situations.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

New lower and upper bounds on Armstrong codes

2020 ◽  
Author(s):  
Todorka Alexandrova ◽  
Peter Boyvalenkov ◽  
Attila Sali
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds
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