Add to ORKGLet x = (x1, x2,...,xn) be a vector in the space Zn with Z ring of integers and q be a positive integer, f a polynomial in x with coefficients in Z. The exponential sum associated with f is defined as S(f;q) = Σ xmodqe(2πif(x)/q) where the sum is taken over a complete set of residues modulo q. The value of S(f;q) depend on the estimate of the cardinality V , the number of elements contained in the set V={Xmodq fx≡ 0 mod q} where fx is the partial derivatives of f with respect to x. To determine the cardinality of V, the p-adic sizes of common zeros of the partial derivative polynomials need to be obtained. In this paper we estimate the p-adic sizes of common zeros of partial derivative polynomials of f(x,y) in Zp(x,y) of degree nine by u...
Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential sums associate...
Let f = f(x,y) be a function of two variables. Let q be an integer and let S(f;q) = ∑x mod qe 2πif(x...
Let x = (x1, x2,..., xn) be a vector in the space ℚn with ℚ field of rational numbers and q be a pos...
Let x=(x1,x2,...,xn) be a vector in a space Zn where Z is the ring of integers and let q be a positi...
Let x = (x1, x2,...,xn) be a vector in a space Zn where Z is the ring of integers and let q be a pos...
Let x =(x1,x2,…,xn) be a vector in the space Q n with Q field of rational numbers and q be a positiv...
The exponential sum associated with f is defined as S (f; q) = ∑x mod q , where the sum is taken ove...
It is known that the value of the exponential sum can be derived from the estimate of the cardinalit...
It is known that the value of the exponential sum S(f;pα) depends on the estimate of the cardinality...
In this paper we obtain an estimation of p-adic sizes of common zeros of partial derivative polynomi...
In this paper we apply Newton polyhedron technique in estimating the p-adic sizes of common zeros of...
Let p be a prime number and f (x, y) be a polynomial in Zp[x, y]. For α > 1, the exponential sums as...
Let p be a prime and f(x, y) be a polynomial in Zp[x, y]. For α > 1, the exponential sums associated...
In this paper we determined the estimate of p-adic sizes of common zeros of partial derivative polyn...
Let p be a prime and f (x, y) be a polynomial in Zp[x, y]. It is defined that the exponential sums a...
Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential sums associate...
Let f = f(x,y) be a function of two variables. Let q be an integer and let S(f;q) = ∑x mod qe 2πif(x...
Let x = (x1, x2,..., xn) be a vector in the space ℚn with ℚ field of rational numbers and q be a pos...
Let x=(x1,x2,...,xn) be a vector in a space Zn where Z is the ring of integers and let q be a positi...
Let x = (x1, x2,...,xn) be a vector in a space Zn where Z is the ring of integers and let q be a pos...
Let x =(x1,x2,…,xn) be a vector in the space Q n with Q field of rational numbers and q be a positiv...
The exponential sum associated with f is defined as S (f; q) = ∑x mod q , where the sum is taken ove...
It is known that the value of the exponential sum can be derived from the estimate of the cardinalit...
It is known that the value of the exponential sum S(f;pα) depends on the estimate of the cardinality...
In this paper we obtain an estimation of p-adic sizes of common zeros of partial derivative polynomi...
In this paper we apply Newton polyhedron technique in estimating the p-adic sizes of common zeros of...
Let p be a prime number and f (x, y) be a polynomial in Zp[x, y]. For α > 1, the exponential sums as...
Let p be a prime and f(x, y) be a polynomial in Zp[x, y]. For α > 1, the exponential sums associated...
In this paper we determined the estimate of p-adic sizes of common zeros of partial derivative polyn...
Let p be a prime and f (x, y) be a polynomial in Zp[x, y]. It is defined that the exponential sums a...
Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential sums associate...
Let f = f(x,y) be a function of two variables. Let q be an integer and let S(f;q) = ∑x mod qe 2πif(x...
Let x = (x1, x2,..., xn) be a vector in the space ℚn with ℚ field of rational numbers and q be a pos...