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Sums and Products from a Finite Set of Real Numbers
The Ramanujan Journal, 1998Let \(A\) be a set of real numbers. Put \(hA=\{x_1+x_2+ \cdots +x_h \mid x_i\in A\}\) and \(A^h=\{x_1x_2 \cdots x_h \;| \;x_i\in A\}\). The author deals with a conjecture of P. Erdős stating that \(hA\cup A^h\) has large cardinality. As observed at the end of the paper, the best results known on this conjecture are due to \textit{G. Elekes} [Acta Arith.
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Sum-Product Estimates Applied to Waring's Problem over Finite Fields
Integers, 2012Abstract ...
Todd Cochrane, James Cipra
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IDENTITIES FOR PRODUCTS OF GAUSS SUMS OVER FINITE FIELDS
1981Several interesting identities are found and proved for Gauss sums defined over finite fields. With \(\zeta=\exp(2\pi i/p)\), \(p\) a prime, define the Gauss some over \(\mathrm{GF}(p^r)\) \((r\geq 1)\) by \[ G(\chi)=G_r(\chi)=-\sum_{x\in\mathrm{GF}(p^r)} \chi(x)\zeta^{\mathrm{Tr}(x)} \] where \(\mathrm{Tr}\) is the trace map from \(\mathrm{GF}(p^r ...
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On the Evaluation of Certain Finite Sums of Progressive Products
The Journal of the Royal Aeronautical Society, 1959This note is concerned with the evaluation of the finite sumwhere the m quantities Zi are arbitrary and whereis the binomial coefficient in a series of n terms. Summations of this kind appear in the evaluation of matrix products involving the reciprocal of order n of a segment of a Hilbert matrix or of a generalised Hilbert matrix.
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Another sum-product estimate in finite fields
Proceedings of the Steklov Institute of Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Finite Trigonometric Product and Sum Identities
The Fibonacci Quarterly, 2012openaire +1 more source