Add to ORKGFor n a positive integer, the Prouhet-Tarry-Escott Problem asks for two different sets of n positive integers for which the sum of the kth powers of the elements of one set is equal to the sum of the kth powers of the elements of the second set for each positive integer k \u3c n. For n \u3e 12, it is not known whether such sets exist. I will give some background on this problem and then show how Newton polygons can be used to determine information on the size of the 2-adic value of a certain constant associated with the problem
AbstractIn this paper we develop a method for determining the number of integers without large prime...
It has recently been shown that a rational specialization of Jacobi polynomials, when reduced modulo...
AbstractIn this paper, it is proved that every sufficiently large odd integer is a sum of a prime, f...
For n a positive integer, the Prouhet-Tarry-Escott Problem asks for two different sets of n positive...
This thesis offers a clear introduction to p-adic number fields, and the method of Newton polygons t...
The classical Newton polygon is a device for computing the fractional power series expansions of alg...
This dissertation considers three different topics. In the first part of the dissertation, we use Ne...
This thesis is concerned with finding integer solutions to certain Diophantine equations. In doing s...
The numbers 1, 2, and 6 have the same sum and same sum of squares as 0, 4, 5. These two sets are sol...
AbstractIn this article we discuss how close different powers of integers can be to each other. In a...
One can associate to any bivariate polynomial P(X,Y) its Newton polygon. This is the convex hull of ...
AbstractLet Fq be the finite field of q elements with characteristic p and Fqm its extension of degr...
AbstractIt is shown that if λ1,…, λ6 are nonzero real numbers, not all of the same sign, such that λ...
This is a survey on sum-product formulae and methods. We state old and new results. Our main objecti...
Let p be a prime and f(x, y) be a polynomial in Zp[x, y]. For α > 1, the exponential sums associated...
AbstractIn this paper we develop a method for determining the number of integers without large prime...
It has recently been shown that a rational specialization of Jacobi polynomials, when reduced modulo...
AbstractIn this paper, it is proved that every sufficiently large odd integer is a sum of a prime, f...
For n a positive integer, the Prouhet-Tarry-Escott Problem asks for two different sets of n positive...
This thesis offers a clear introduction to p-adic number fields, and the method of Newton polygons t...
The classical Newton polygon is a device for computing the fractional power series expansions of alg...
This dissertation considers three different topics. In the first part of the dissertation, we use Ne...
This thesis is concerned with finding integer solutions to certain Diophantine equations. In doing s...
The numbers 1, 2, and 6 have the same sum and same sum of squares as 0, 4, 5. These two sets are sol...
AbstractIn this article we discuss how close different powers of integers can be to each other. In a...
One can associate to any bivariate polynomial P(X,Y) its Newton polygon. This is the convex hull of ...
AbstractLet Fq be the finite field of q elements with characteristic p and Fqm its extension of degr...
AbstractIt is shown that if λ1,…, λ6 are nonzero real numbers, not all of the same sign, such that λ...
This is a survey on sum-product formulae and methods. We state old and new results. Our main objecti...
Let p be a prime and f(x, y) be a polynomial in Zp[x, y]. For α > 1, the exponential sums associated...
AbstractIn this paper we develop a method for determining the number of integers without large prime...
It has recently been shown that a rational specialization of Jacobi polynomials, when reduced modulo...
AbstractIn this paper, it is proved that every sufficiently large odd integer is a sum of a prime, f...