scientific article; zbMATH DE number 918589

zbMath0856.11038MaRDI QIDQ4888817

Anatolii A. Karatsuba

Publication date: 21 August 1996

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zbMATH Keywords

generating functionsRiemann zeta-functionRiemann's hypothesisdensity theoremsDirichlet \(L\)-functionstrigonometric sumssummation formulacomplex integration methodzeros on the critical lineanalytic number theoryclass numbers of binary quadratic formsprime numbers in arithmetic progressionsapplications of complex analysis to number theoryapproximating equations of the Riemann zeta-functionboundary of zerosreal zeros of \(L\)-functions

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) (zeta (s)) and (L(s, chi)) (11M06) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Primes in congruence classes (11N13)

Related Items (12)

New summation and transformation formulas of the Poisson, Müntz, Möbius and Voronoi type ⋮ On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s ⋮ Zero multiplicity and lower bound estimates of \(|\zeta(S)|\) ⋮ Unnamed Item ⋮ On a version of the Hua problem ⋮ Scientific achievements of Anatolii Alekseevich Karatsuba ⋮ A property of the set of primes as a multiplicative basis of the natural numbers ⋮ Comments to my works, written by myself ⋮ The Hurwitz zeta function as a convergent series ⋮ Prime simplicity ⋮ Universality and summability of Dirichlet series ⋮ Jacob's ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations

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