Application of Vandermonde Determinant in Advanced Algebra Solving

2021 ◽  
Vol 11 (07) ◽  
pp. 1421-1429
Author(s):  
雯燕 徐
Keyword(s):  
Vandermonde Determinant

Extreme Points of the Vandermonde Determinant on Surfaces Implicitly Determined by a Univariate Polynomial

2020 ◽  
pp. 791-818
Author(s):  
Asaph Keikara Muhumuza ◽  
Karl Lundengård ◽  
Jonas Österberg ◽  
Sergei Silvestrov ◽  
John Magero Mango ◽  
...  
Keyword(s):  
Extreme Points ◽  
Vandermonde Determinant ◽  
Univariate Polynomial

GOWERS UNIFORMITY NORM AND PSEUDORANDOM MEASURES OF THE PSEUDORANDOM BINARY SEQUENCES

2011 ◽  
Vol 07 (05) ◽  
pp. 1279-1302 ◽  
Author(s):  
HUANING LIU
Keyword(s):  
Exponential Sums ◽  
Binary Sequences ◽  
Vandermonde Determinant ◽  
Additive Character ◽  
Pseudorandom Sequences ◽  
Multiplicative Inverse ◽  
Large Families ◽  
Points Of View ◽  
Pseudorandom Measures ◽  
Gowers Norm

Recently there has been much progress in the study of arithmetic progressions. An important tool in these developments is the Gowers uniformity norm. In this paper we study the Gowers norm for pseudorandom binary sequences, and establish some connections between these two subjects. Some examples are given to show that the "good" pseudorandom sequences have small Gowers norm. Furthermore, we introduce two large families of pseudorandom binary sequences constructed by the multiplicative inverse and additive character, and study the pseudorandom measures and the Gowers norm of these sequences by using the estimates of exponential sums and properties of the Vandermonde determinant. Our constructions are superior to the previous ones from some points of view.

scholarly journals On a problem related to the Vandermonde determinant

2009 ◽  
Vol 157 (13) ◽  
pp. 2997-2999 ◽  
Author(s):  
Tomohiro Sogabe ◽  
Moawwad El-Mikkawy
Keyword(s):  
Vandermonde Determinant

A NONVANISHING LEMMA FOR CERTAIN PADÉ APPROXIMATIONS OF THE SECOND KIND

2011 ◽  
Vol 07 (08) ◽  
pp. 1977-1997
Author(s):  
VILLE MERILÄ
Keyword(s):  
Diophantine Approximation ◽  
Algebraic Number ◽  
Hypergeometric Functions ◽  
Linear Independence ◽  
Number Fields ◽  
Vandermonde Determinant ◽  
Algebraic Number Fields ◽  
Padé Approximations ◽  
Pade Approximations

We prove the nonvanishing lemma for explicit second kind Padé approximations to generalized hypergeometric and q-hypergeometric functions. The proof is based on an evaluation of a generalized Vandermonde determinant. Also, some immediate applications to the Diophantine approximation is given in the form of sharp linear independence measures for hypergeometric E- and G-functions in algebraic number fields with different valuations.

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