Related papers: Large quadratic character sums with multiplicative…

Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli…

Let $Q(x,y,z)$ be an integral quadratic form with determinant coprime to some modulus $q$. We show that $q\mid Q$ for some non-zero integer vector $(x,y,z)$ of length $O(q^{5/8+\varepsilon})$, for any fixed $\varepsilon>0$. Without the…

In this paper, we prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain $L$-series.

We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce…

In this article, we obtain the analytic continuation of the multiple shifted Lucas zeta function, multiple Lucas $L$-function associated to Dirichlet characters and additive characters. We then compute a complete list of exact singularities…

We show that certain sums studied in two recent papers are basically character coordinates (as they are called in the literature). These sums involve values of Dirichlet characters and powers of $\cot(\pi k/n)$, $1\le k\le n-1$. We also…

In this paper, we obtain under the assumption of the Generalized Riemann Hypothesis upper bounds for all high integral moments of sums of Fourier coefficients of a given modular form twisted by quadratic Dirichlet characters. We show the…

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are…

We evaluate the first moment of central values of the family of quadratic Dirichlet $L$-functions using the method of double Dirichlet series. Under the generalized Riemann hypothesis, we prove an asymptotic formula with an error term of…

We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interval, whose admissible length depends on whether or not we…

The main purpose of this paper is to study higher order moments of the generalized quadratic Gauss sums weighted by $L$-functions using estimates for character sums and analytic methods. We find asymptotic formulas for three character sums…

In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…

In this paper we generalize a result of Montgomery and Vaughan regarding exponential sums with multiplicative coefcients to the setting of Weyl sums. As applications, we establish a joint equidistribution result for roots of polynomial…

We study smoothed character sums involving $\sum_{m,n} ( \frac{m}{n} )_2$, where $( \frac{m}{n} )_2$ denotes the quadratic symbol in the Gaussian field. We extend previously known results to obtain asymptotic formulas for the sums…

The purpose of this paper is to give some explicit formulas involving M\"obius functions, which may be known under the generalized Riemann Hypothesis, but unconditional in this paper. Concretely, we prove explicit formulas of partial sums…

We obtain nontrivial estimates of quadratic character sums of division polynomials $\Psi_n(P)$, $n=1,2, ...$, evaluated at a given point $P$ on an elliptic curve over a finite field of $q$ elements. Our bounds are nontrivial if the order of…

The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series which involves a product of Riemann zeta-functions of a special form.

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 prove that an innocent looking inequality implies the Riemann Hypothesis and show a way to approach this inequality through sums of Legendre symbols.

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…