Related papers: Explicit Burgess Bound for Composite Moduli

We prove that Burgess's bound gives an estimate not just for a single character sum, but for a mean value of many such sums.

In this work we establish a Burgess bound for short multiplicative character sums in arbitrary dimensions, in which the character is evaluated at a homogeneous form that belongs to a very general class of "admissible" forms. This…

This paper proves Burgess bounds for short mixed character sums in multi-dimensional settings. The mixed character sums we consider involve both an exponential evaluated at a real-valued multivariate polynomial, and a product of…

We obtain a Burgess-type bound for character sums over unions of intervals. The result follows from the argument of Heath-Brown, with an improvement in one of the steps.

This work proves a Burgess bound for short mixed character sums in $n$ dimensions. The non-principal multiplicative character of prime conductor $q$ may be evaluated at any "admissible" form, and the additive character may be evaluated at…

This paper proves nontrivial bounds for short mixed character sums by introducing estimates for Vinogradov's mean value theorem into a version of the Burgess method.

In this paper we consider the problem of estimating character sums to composite modulus and obtain some progress towards removing the cubefree restriction in the Burgess bound. Our approach is to estimate high order moments of character…

We prove character sum estimates for additive Bohr subsets modulo a prime. These estimates are analogous to classical character sum bounds of Polya-Vinogradov and Burgess. These estimates are applied to obtain results on recurrence mod $p$…

In this paper we give a refinement of the bound of D. A. Burgess for multiplicative character sums modulo a prime number $q$. This continues a series of previous logarithmic improvements, which are mostly due to H. Iwaniec and E. Kowalski.…

We establish Burgess-type bounds for short multiplicative character sums over finite fields $\mathbb{F}_{p^n}$ under a purely volumetric condition. We show that for a box $B \subset \mathbb{F}_{p^n}$, nontrivial cancellation occurs whenever…

We show that even mild improvements of the Polya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of…

Burgess proved that for $\chi_q$ a primitive Dirichlet character modulo $q$ with $q$ cubefree, $\Big|\sum_{M< n\le M+N}\chi_q(n)\Big| \ll N^{1-\frac{1}{r}}q^{\frac{r+1}{4r^2}+\epsilon}$ for all integers $r\ge1.$ More recently, explicit…

Let $\chi$ be a Dirichlet character modulo $p$, a prime. In applications, one often needs estimates for short sums involving $\chi$. One such estimate is the family of bounds known as \emph{Burgess' bound}. In this paper, we explore several…

We propose upper bounds for the number of modular constituents of the restriction modulo $p$ of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.

We establish new estimates on short character sums for arbitrary composite moduli with small prime factors. Our main result improves on the Graham-Ringrose bound for square free moduli and also on the result due to Gallagher and Iwaniec…

We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.

We prove explicit bounds for the number of sums of consecutive prime squares below a given magnitude.

We prove an extension of the Bourgain-Sarnak-Ziegler theorem and then apply it to bound certain polynomial exponential sums with modular coefficients.

We use GL(2) delta method to establish the Burgess bound.

In this paper, we give a constant $C$ in \cite[Theorem 1.2]{sha2014bounding} by using an explicit Baker's inequality, hence we have an explicit bound of the integral points on modular curves.