scientific article

zbMath0971.11001MaRDI QIDQ2703226

M. Ram Murty

Publication date: 1 March 2001

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

zbMATH Keywords

prime number theoremHadamard productscontour integrationSelberg classDirichlet charactersexplicit formulaeHensel lemmaAbel's summation\(p\)-adic zeta functionfunctional equation of the zeta functionMöbius formulaorder of arithmetic functionszeros of the zeta-function

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Arithmetic functions; related numbers; inversion formulas (11A25) Primes (11A41) Zeta and (L)-functions in characteristic (p) (11M38) Sieves (11N35) Multiplicative number theory (11Nxx) Entire and meromorphic functions of one complex variable, and related topics (30Dxx) Zeta and (L)-functions: analytic theory (11Mxx)

Related Items (26)

Joint universality for Dirichlet \(L\)-functions and zeros of their linear combinations in the \(\chi \)-aspect ⋮ Cyclicity of CM elliptic curves modulo 𝑝 ⋮ On the Vanishing of TwistedL-Functions of Elliptic Curves ⋮ On the number of special numbers ⋮ On certain sums of number theory ⋮ Effective uniform approximation by \(L\)-functions in the Selberg class ⋮ Universality for \(L\)-functions in the Selberg class ⋮ Counting rational points on projective varieties ⋮ Values of Dirichlet \(L\)-functions, Gauss sums and trigonometric sums ⋮ Sign changes of Fourier coefficients of Siegel cusp forms of degree two on Hecke congruence subgroups ⋮ Mean values of \(L\)-functions and Dedekind sums ⋮ Reciprocity laws for Dedekind cotangent sums ⋮ On asymptotic behavior of generalized Li coefficients ⋮ Bounds for generalized Sidon sets ⋮ The fourth power mean of Dirichlet \(L\)-functions in \(\mathbb{F}_q [T\)] ⋮ The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms ⋮ A Barban-Davenport-Halberstam asymptotic for number fields ⋮ Representations of integers by certain positive definite binary quadratic forms ⋮ On Li's criterion for the Riemann hypothesis for the Selberg class ⋮ Denominator-preserving maps ⋮ Euler’s function on products of primes in a fixed arithmetic progression ⋮ A family of number fields with unit rank at least 4 that has Euclidean ideals ⋮ A variant of the Bombieri-Vinogradov theorem with explicit constants and applications ⋮ Simultaneous non-vanishing of twists ⋮ On the cyclicity of the group of \({\mathbb F}_p\)-rational points of non-CM elliptic curves ⋮ A weighted Turán sieve method

This page was built for publication: