Results 31 to 40 of about 7,643 (187)
ON SUM OF PRODUCTS AND THE ERDŐS DISTANCE PROBLEM OVER FINITE FIELDS [PDF]
Bulletin of the Australian Mathematical Society, 2011 AbstractFor a prime powerq, let 𝔽qbe the finite field ofqelements. We show that 𝔽*q⊆d𝒜2for almost every subset 𝒜⊂𝔽qof cardinality ∣𝒜∣≫q1/d. Furthermore, ifq=pis a prime, and 𝒜⊆𝔽pof cardinality ∣𝒜∣≫p1/2(logp)1/d, thend𝒜2contains both large and small residues. We also obtain some results of this type for the Erdős distance problem over finite fields.
Lê Anh Vinh
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Symmetry, 2018 Here we consider sums of finite products of Chebyshev polynomials of the third and fourth kinds. Then we represent each of those sums of finite products as linear combinations of the four kinds of Chebyshev polynomials which involve the hypergeometric ...
Taekyun Kim +3 more
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Multi-parameter projection theorems with applications to sums-products and finite point configurations in the Euclidean setting [PDF]
, 2011 In this chapter we study multiparameter projection theorems for fractal sets. With the help of these estimates, we recover results about the size of \(A \cdot A + \cdots+ A \cdot A\), where A is a subset of the real line of a given Hausdorff dimension, \(
B. Erdoğan, D. Hart, A. Iosevich
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Shintani’s zeta function is not a finite sum of Euler products [PDF]
Proceedings of the American Mathematical Society, 2014 We prove that the Shintani zeta function associated to the space of binary cubic forms cannot be written as a finite sum of Euler products. Our proof also extends to several closely related Dirichlet series. This answers a question of Wright in the negative.
Frank Thorne
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Finite sums of products of functions in single variables
Linear Algebra and its Applications, 1990 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. Neuman
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Finite sums of Toeplitz products on the Dirichlet space
Journal of Mathematical Analysis and Applications, 2009 The paper deals with a class of operators on the Dirichlet space of the unit disk which contain finite sums of products of two Toeplitz operators with harmonic symbols. The author presents characterizations for these operators to be zero and compact, and provides an answer to the ``zero-product'' problem for products of finitely many Toeplitz operators
Y. J. Lee
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ON THE SOLVABILITY OF SYSTEMS OF SUM–PRODUCT EQUATIONS IN FINITE FIELDS [PDF]
Glasgow Mathematical Journal, 2011 AbstractIn an earlier paper, for ‘large’ (but otherwise unspecified) subsets , , , of q, Sárközy showed the solvability of the equations a + b = cd with a ∈ , b ∈ , c ∈ , d ∈ . This equation has been studied recently by many other authors. In this paper, we study the solvability of systems of equations of this type using additive character sums.
Lê Anh Vinh
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Finite rank sums of products of Toeplitz and Hankel operators
Journal of Mathematical Analysis and Applications, 2013 AbstractOn the Dirichlet space of the unit disk, we consider operators which are finite sums of Toeplitz products, Hankel products or products of Toeplitz and Hankel operators. We then give characterizations of when such operators have finite rank on the Dirichlet space.
Y. J. Lee
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Low-rank sum-of-products finite-basis-representation (SOP-FBR) of potential energy surfaces [PDF]
The Journal of Chemical Physics, 2020 The sum-of-products finite-basis-representation (SOP-FBR) approach for the automated multidimensional fit of potential energy surfaces (PESs) is presented. In its current implementation, the method yields a PES in the so-called Tucker sum-of-products form, but it is not restricted to this specific ansatz.
Ramón L. Panadés‐Barrueta +1 more
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Some Identities on Sums of Finite Products of the Pell, Fibonacci, and Chebyshev Polynomials
Indian Journal of Science and Technology, 2023 Jugal Kishore, Vipin Verma
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