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An Adaptive Collocation Method for Solving Delay Fractional Differential Equations
In this article, an adaptive collocation method is investigated for solving delay fractional differential equations (DFDEs). The fractional...
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The sums of exceptional units in a finite ring
We prove a formula for the number of representations of an element in a finite basic ring as a sum of k exceptional units and find bounds for this...
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Evaluation of a Class of Quadratic Gauss Sums by Sampling a Continuous Chirp Signal
The calculation of Discrete Fourier Transform (DFT) of a periodic discrete-time chirp ends in the evaluation of a quadratic Gauss sum. The...
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Multiplicative character sums of Fermat quotients and pseudorandom sequences
We prove a bound on sums of products of multiplicative characters of shifted Fermat quotients modulo p . From this bound we derive results on the...
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Sign or root of unity ambiguities of certain Gauss sums
Gauss sums play an important role in number theory and arithmetic geometry. The main objects of study in this paper are Gauss sums over the finite...
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Constructing quasi-random subsets of ℤ N by using elliptic curves
Let ɛ : y 2 = x 3 + Ax + B be an elliptic curve defined over the finite field ℤ p ( p > 3) and G be a rational point of prime order N on E . Define a...
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Higher-Order Fourier Analysis Of \({\mathbb{F}_{p}^n}\) And The Complexity Of Systems Of Linear Forms
In this article we are interested in the density of small linear structures (e.g. arithmetic progressions) in subsets A of the group
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A Prime Sensitive Hankel Determinant of Jacobi Symbol Enumerators
We show that the determinant of a Hankel matrix of odd dimension n whose entries are the enumerators of the Jacobi symbols which depend on the row...
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On the pseudorandomness of binary and quaternary sequences linked by the gray map**
Binary and quaternary sequences are the most important sequences in view of many practical applications. Any quaternary sequence can be decomposed...
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A new sieve for distinct coordinate counting
We present a new sieve for the distinct coordinate counting problem. This significantly improves the classical inclusion-exclusion sieve for this...
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Complexity of prime-dimensional sequences over a finite field
V. I. Arnold has recently defined the complexity of a sequence of n zeros and ones with the help of the operator of finite differences. In this paper...
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On pseudorandom properties of some Dirichlet characters
In this paper, we try to generalize the Mauduit–Sárközy pseudorandom properties of the Legendre symbol to Dirichlet characters. We prove that in our...
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Equations in finite fields with restricted solution sets. I (Character sums)
In earlier papers, for “large” (but otherwise unspecified) subsets A , B of Z p and for h ( x ) ∈ Z p [ x ], Gyarmati studied the solvability of the...