61 citations · 445 across the 59 of their papers we have counts for
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Algebraic independence of Mahler functions via radial asymptotics
Richard P. Brent, Michael Coons, Wadim Zudilin
We present a new method for algebraic independence results in the context of Mahler's method. In particular, our method uses the asymptotic behaviour of a Mahler function as…
Some binomial sums involving absolute values
Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn +1
We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form \[S_{α,β}…
Generalising Tuenter's binomial sums
Richard P. Brent
Tuenter [Fibonacci Quarterly 40 (2002), 175-180] and other authors have considered centred binomial sums of the form \[S_r(n) = \sum_k \binom{2n}{k}|n-k|^r,\] where and are…
Lower bounds on maximal determinants of binary matrices via the probabilistic method
Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith
Let be the maximal determinant for -matrices, and be the ratio of to the Hadamard upper bound. We give severa…
Bounds on determinants of perturbed diagonal matrices
Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith
We give upper and lower bounds on the determinant of a perturbation of the identity matrix or, more generally, a perturbation of a nonsingular diagonal matrix. The matrices conside…