Results 1 to 10 of about 248 (85)
Diophantine equations in separated variables and polynomial power sums. [PDF]
Mon Hefte Math, 2021 We consider Diophantine equations of the shape f(x)=g(y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Fuchs C, Heintze S.
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Quantitative results on Diophantine equations in many variables [PDF]
Acta Arithmetica, 2020 We consider a system of integer polynomials of the same degree with non-singular local zeros and in many variables. Generalising the work of Birch (1962) we find quantitative asymptotics (in terms of the maximum of the absolute value of the coefficients of these polynomials) for the number of integer zeros of this system within a growing box.
J. V. Ittersum
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Diophantine equations in moderately many variables [PDF]
Michigan Mathematical Journal, 2016 We give upper bounds for the number of integral solutions of bounded height to a system of equations $f_i(x_1,\ldots,x_n) = 0$, $1 \leq i \leq r$, where the $f_i$ are polynomials with integer coefficients. The estimates are obtained by generalising an approach due to Heath-Brown, using a certain $q$-analogue of van der Corput's method, to the case of ...
Oscar Marmon
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Optimization of the multivariate polynomial public key for quantum safe digital signature [PDF]
Scientific Reports, 2023 Kuang, Perepechaenko, and Barbeau recently proposed a novel quantum-safe digital signature algorithm called Multivariate Polynomial Public Key or MPPK/DS.
Randy Kuang, Maria Perepechaenko
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Arithmetic of arithmetic Coxeter groups. [PDF]
Proc Natl Acad Sci U S A, 2019 Significance Conway’s topograph provided a combinatorial-geometric perspective on integer binary quadratic forms—quadratic functions of two variables with integer coefficients.
Milea S, Shelley CD, Weissman MH.
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Counting monochromatic solutions to diagonal Diophantine equations
Discrete Analysis, 2021 Counting monochromatic solutions to diagonal Diophantine equations, Discrete Analysis 2021:14, 47 pp. An important subfield of Ramsey theory concerns questions of the following type: for which systems of equations $E_1,\dots,E_k$ in variables $x_1,\dots,
Sean Prendiville
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PRIME SOLUTIONS TO POLYNOMIAL EQUATIONS IN MANY VARIABLES AND DIFFERING DEGREES [PDF]
Forum of Mathematics, Sigma, 2017 Let $\mathbf{f}=(f_{1},\ldots ,f_{R})$ be a system of polynomials with integer coefficients in which the degrees need not all be the same. We provide sufficient conditions for which the system of equations $f_{j}(x_{1},\ldots ,x_{n})=0~(1\leqslant j ...
S. Yamagishi
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AN APPLICATION OF LINEAR DIOPHANTINE EQUATIONS TO CRYPTOGRAPHY
Advances in Mathematics: Scientific Journal, 2021 In this chapter we propose a Key exchange protocol based on a random solution of linear Diophantine equation in n variables, where the considered linear Diophantine equation satisfies the condition for existence of infinitely many solutions.
P. Kameswari +2 more
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Diophantine equations in separated variables and lacunary polynomials [PDF]
, 2017 We study Diophantine equations of type f(x) = g(y), where f and g are lacunary polynomials. According to a well-known finiteness criterion, for a number field K and nonconstant f,g ∈ K[x], the equation f(x) = g(y) has infinitely many solutions in S ...
D. Kreso
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