scientific article

Publication date: 25 October 2011

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

prime number theorem $l$-adic cohomology Weil conjectures Sato-Tate conjecture Chebotarev density theorem Frobenian sets

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Varieties over global fields (11G35) Global ground fields in algebraic geometry (14G25) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27)

Related Items (67)

Diagonal quartic surfaces with a Brauer–Manin obstruction ⋮ On the Bertini regularity theorem for arithmetic varieties ⋮ Ordinary primes for abelian surfaces ⋮ Density questions on arithmetic equivalence ⋮ Kirillov's orbit method and polynomiality of the faithful dimension of $p$-groups ⋮ Multivariate normal distribution for integral points on varieties ⋮ Stability results for local zeta functions of groups algebras, and modules ⋮ A Framework for Computing Zeta Functions of Groups, Algebras, and Modules ⋮ The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3 ⋮ Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map ⋮ Distribution of integral values for the ratio of two linear recurrences ⋮ Quantitative arithmetic of diagonal degree 2 $K3$ surfaces ⋮ On Hilbert’s irreducibility theorem for linear algebraic groups ⋮ Exceptional splitting of reductions of abelian surfaces ⋮ Generic elements of a Zariski-dense subgroup form an open subset ⋮ Arithmetic statistics of Prym surfaces ⋮ Surface bundles and the section conjecture ⋮ Arithmetic inflection formulae for linear series on hyperelliptic curves ⋮ Chebotarev-Sato-Tate distribution for abelian surfaces potentially of $\mathrm{GL}_2$-type ⋮ Classification of singular del Pezzo surfaces over finite fields ⋮ Cohomology of moduli spaces of Del Pezzo surfaces ⋮ Hemisystems of the Hermitian surface ⋮ Unnamed Item ⋮ On a local-global principle for quadratic twists of abelian varieties ⋮ Sato-Tate distributions of Catalan curves ⋮ Distribution of genus numbers of abelian number fields ⋮ Geometric structures in group theory. Abstracts from the workshop held February 27 -- March 5, 2022 ⋮ Counting invertible Schrödinger operators over finite fields for trees, cycles and complete graphs ⋮ Modular forms mod 2: structure of the Hecke ring ⋮ Unnamed Item ⋮ Sato-Tate distributions ⋮ Arbitrarily long gaps between the values of positive‐definite cubic and biquadratic diagonal forms ⋮ Sieving rational points on varieties ⋮ The Sato-Tate conjecture for a Picard curve with complex multiplication (with an appendix by Francesc Fité) ⋮ Fields of definition of elliptic $k$-curves and the realizability of all genus 2 Sato–Tate groups over a number field ⋮ Computing local zeta functions of groups, algebras, and modules ⋮ Cycles in the de Rham cohomology of abelian varieties over number fields ⋮ Towards the Sato–Tate groups of trinomial hyperelliptic curves ⋮ Quantifying residual finiteness of linear groups ⋮ A finite analogue of the ring of algebraic numbers ⋮ Arithmetic invariants from Sato-Tate moments ⋮ The twisting Sato-Tate group of the curve $y^2 = x^{8} - 14x^4 + 1$ ⋮ An Erdős-Kac law for local solubility in families of varieties ⋮ Sato-Tate distributions on Abelian surfaces ⋮ Ordinary primes in Hilbert modular varieties ⋮ The Frobenius traces distribution for modular abelian surfaces ⋮ Del Pezzo surfaces over finite fields and their Frobenius traces ⋮ Spins of prime ideals and the negative Pell equation ⋮ SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN -FUNCTIONS ⋮ Sato-Tate distributions of twists of the Fermat and the Klein quartics ⋮ The distribution of the trace in the compact group of type 𝐆₂ ⋮ Sato-Tate distributions of $y^2=x^p-1$ and $y^2=x^{2p}-1$ ⋮ On the moments of torsion points modulo primes and their applications ⋮ Statistics of the first Galois cohomology group: a refinement of Malle's conjecture ⋮ The Sato-Tate conjecture and Nagao's conjecture ⋮ Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms ⋮ On compatibility of the $\ell$-adic realisations of an abelian motive ⋮ Rational points and prime values of polynomials in moderately many variables ⋮ Relations among Ramanujan-type congruences. I ⋮ Counting points on superelliptic curves in average polynomial time ⋮ On the arithmetic of cross-ratios and generalised Mertens' formulas ⋮ On the proportion of locally soluble superelliptic curves ⋮ On the least common multiple of polynomial sequences at prime arguments ⋮ On the Sato-Tate conjecture for non-generic abelian surfaces ⋮ Congruences like Atkin’s for the partition function ⋮ Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type ⋮ Computing 𝐿-polynomials of Picard curves from Cartier–Manin matrices

This page was built for publication: