scientific article; zbMATH DE number 1994516

Publication date: 20 October 2003

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Estimates on exponential sums (11L07) Asymptotic results on arithmetic functions (11N37) (zeta (s)) and (L(s, chi)) (11M06) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Estimates on character sums (11L40)

Related Items (98)

An Introduction to Riemann’s Life, His Mathematics, and His Work on the Zeta Function ⋮ An exponential sum involving Fourier coefficients of eigenforms for $\mathrm{SL}(2,\mathbb{Z})$ ⋮ Multiplicative functions in short intervals ⋮ A weighted divisor problem ⋮ Gram's law in the theory of the Riemann zeta-function. I ⋮ DENOMINATORS OF BERNOULLI POLYNOMIALS ⋮ Number of prime factors with a given multiplicity ⋮ Power moments and value distribution of functions ⋮ An approximate functional equation for the primitive of Hardy's function ⋮ On the distribution of square-full numbers in arithmetic progressions ⋮ On sums of sums involving cube-full numbers ⋮ On the universality of the Epstein zeta function ⋮ On the Riesz means of \frac nφ(n) – III ⋮ On the value-distribution of Hurwitz zeta-functions with algebraic parameter ⋮ Riemann-type functional equations: Dirichlet polynomial approximations and a weak Gram law ⋮ Infinitely log-monotonic combinatorial sequences ⋮ Uniform mean value estimates and discrete Hilbert inequalities via orthogonal Dirichlet series ⋮ The first moment of $L$-functions of primitive forms on $\Gamma _{0}(p^\alpha )$ and a basis of old forms ⋮ On the multiplicities of zeros of $\zeta(s)$ and its values over short intervals ⋮ Spectral large sieve inequalities for Hecke congruence subgroups of $\mathrm{SL}(2,\mathbb{Z}[i)$] ⋮ From the Ideal Theorem to the class number ⋮ On primes, almost primes, and the Möbius function in short intervals ⋮ Counting elliptic curves over the rationals with a 7-isogeny ⋮ Higher uniformity of arithmetic functions in short intervals I. All intervals ⋮ The average order of Hecke eigenvalues of Siegel cusp forms of genus 2 ⋮ Applications of Wirtinger inequalities on the distribution of zeros of the Riemann zeta-function ⋮ A note on the Fourier coefficients of Hecke-Maass forms ⋮ Van der Corput method and optical illusions ⋮ Unnamed Item ⋮ Mertens Sums requiring Fewer Values of the Möbius Function ⋮ Estimates for $L$-functions in the critical strip under GRH with effective applications ⋮ Explicit zero density estimate for the Riemann zeta-function near the critical line ⋮ On higher moments of Dirichlet coefficients attached to symmetric square $L$-functions over certain sparse sequence ⋮ Additive properties of subgroups of finite index in fields ⋮ On the Möbius function in all short intervals ⋮ Volterra operators and Hankel forms on Bergman spaces of Dirichlet series ⋮ The distribution of k-free numbers and the derivative of the Riemann zeta-function ⋮ Moments and oscillations of exponential sums related to cusp forms ⋮ Large oscillations of the argument of the Riemann zeta‐function ⋮ Integral mean-square estimation of error terms of Fourier coefficients attached to cusp forms ⋮ Uniform estimates for sums of coefficients of symmetric power $L$-functions ⋮ Improved subconvexity bounds for 𝐺𝐿(2)×𝐺𝐿(3) and 𝐺𝐿(3) 𝐿-functions by weighted stationary phase ⋮ ON MULTIPLICATIVE COMPOSITIONS OF INTEGERS ⋮ The weak Gram law for Hecke $L$-functions ⋮ ON A NEW CIRCLE PROBLEM ⋮ Higher power moments of the Riesz mean error term of symmetric square $L$-function ⋮ Unnamed Item ⋮ Local properties of Hilbert spaces of Dirichlet series ⋮ Multifractal behavior of polynomial Fourier series ⋮ On the Riesz means of $\frac{n}{\varphi(n)}$. II ⋮ Exponential and infinitary divisors ⋮ Uniform estimates for sums of coefficients of symmetric square $L$-function ⋮ On integrals and Dirichlet series obtained from the error term in the circle problem ⋮ Irrational factor of order $k$ and its connections with $k$-free integers ⋮ The divisor function on residue classes II ⋮ Effective universality theorem: a survey ⋮ Fractional differential relations for the Lerch zeta function ⋮ A pair correlation problem, and counting lattice points with the zeta function ⋮ Sparser variance for primes in arithmetic progression ⋮ On the distribution of values of the argument of the Riemann zeta-function ⋮ Riemann's zeta-function and the divisor problem. III ⋮ Visible lattice points in the sphere ⋮ Estimates of a certain sum involving coefficients of cusp forms in weight and level aspects ⋮ On sums involving Fourier coefficients of Maass forms for $\mathrm{SL}(3,\mathbb Z)$ ⋮ On representations of error terms related to the derivatives for some Dirichlet series ⋮ Gram's law in the theory of the Riemann zeta-function. II ⋮ An improvement for the large sieve for square moduli ⋮ Contribution of non integer integro-differential operators (NIDO) to the geometrical understanding of Riemann's conjecture. II ⋮ Local interpolation in Hilbert spaces of Dirichlet series ⋮ Riemann's conjecture and a fractional derivative ⋮ On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces ⋮ A note on cube-full numbers in arithmetic progression ⋮ Square-root cancellation for sums of factorization functions over short intervals in function fields ⋮ The Relative Trace Formula in Analytic Number Theory ⋮ Note on a problem of Ramanujan ⋮ Mean square of the derivatives of Hardy's $Z$-function ⋮ Error term of the mean value theorem for binary Egyptian fractions ⋮ Double Dirichlet series associated with arithmetic functions ⋮ Exponential sums related to Maass forms ⋮ The Lerch zeta function as a fractional derivative ⋮ Linear programming over exponent pairs ⋮ Large positive and negative values of Hardy’s 𝑍-function ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back ⋮ A modified Riemann zeta distribution in the critical strip ⋮ A note on the zeros of the zeta-function of Riemann ⋮ New approximations of the gamma function in terms of the digamma function ⋮ Riemann-type functional equations. Julia line and counting formulae ⋮ Sums of Fourier coefficients of holomorphic cusp forms over integers without large prime factors ⋮ Unnamed Item ⋮ Mean values of long Dirichlet polynomials with higher divisor coefficients ⋮ On discrete mean values of Dirichlet $L$-functions ⋮ Weighted divisor sums and Bessel function series. V. ⋮ Lattice points in the 3-dimensional torus ⋮ Weyl asymptotics for tensor products of operators and Dirichlet divisors ⋮ Atkinson's formula for the mean square of $\zeta (s)$ with an explicit error term ⋮ The average behaviour of the error term in a new kind of the divisor problem ⋮ Estimates for Weyl sums in the theory of discrete universality ⋮ On sums of sums involving squarefull numbers

This page was built for publication: