Estimates for Weyl sums in the theory of discrete universality
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DOI: 10.1007/s11139-020-00381-9
Abstract: We prove joint and disjoint discrete universality theorems for Dirichlet L-functions $$L(s,\chi )$$ and Hurwitz zeta-functions $$\zeta (s;\beta )$$ with rational parameter $$\beta \in (0,1]$$ . Our approach does not utilize Gallagher’s lemma, which is… read more here.
Keywords: discrete universality; universality; weyl sums; estimates weyl ... See more keywords
On large values of Weyl sums
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DOI: 10.1016/j.aim.2020.107216
Abstract: A special case of the Menshov--Rademacher theorem implies for almost all polynomials $x_1Z+\ldots +x_d Z^{d} \in {\mathbb R}[Z]$ of degree $d$ for the Weyl sums satisfy the upper bound $$ \left| \sum_{n=1}^{N}\exp\left(2\pi i \left(x_1 n+\ldots… read more here.
Keywords: weyl sums; large values; values weyl;
Bombieri-type theorems of nonlinear Weyl sums over primes in short intervals
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DOI: 10.1142/s1793042118501531
Abstract: In this paper, we consider the mean-value estimate for nonlinear Weyl sums over primes in short intervals and establish the related Bombieri-type theorems. These results have applications in additive problems with prime variables in short… read more here.
Keywords: nonlinear weyl; sums primes; bombieri type; short intervals ... See more keywords