4 citations · 16 across the 30 of their papers we have counts for
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Metric theory of Weyl sums
Changhao Chen, Bryce Kerr, James Maynard +1
We prove that there exist positive constants and such that for any integer the set of satisfying $$ cN^{1/2}\le \left|\sum^N_{n=1}\exp\le…
On elements of large order of elliptic curves and multiplicative dependent images of rational functions over finite fields
Bryce Kerr, Jorge Mello, Igor E. Shparlinski
Let and be elliptic curves in Legendre form with integer parameters. We show there exists a constant such that for almost all primes, for all but at most pairs…
An effective local-global principle for algebraic varieties and the sum product problem in finite fields
Bryce Kerr, Jorge Mello, Igor Shparlinski
We use recent results about linking the number of zeros on algebraic varieties over , defined by polynomials with integer coefficients, and on their reductions modulo s…
Metric theory of lower bounds on Weyl sums
Changhao Chen, Bryce Kerr, Igor Shparlinski
We prove that the Hausdorff dimension of the set , such that $$ \left|\sum_{n=1}^N \exp\left(2 πi\left(x_1n+\ldots+x_d n^d\right)\right) \right|\ge c N^{1/2}…
On digits of Mersenne numbers
Bryce Kerr, László Mérai, Igor E. Shparlinski
Motivated by recently developed interest to the distribution of -ary digits of Mersenne numbers , where is prime, we estimate rational exponential sums with $M_…