Estimates of $\theta(x;k,l)$ for large values of $x$

DOI10.1090/S0025-5718-01-01351-5zbMath1042.11057MaRDI QIDQ4529710

Pierre Dusart

Publication date: 6 May 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

arithmetic progressionprime numbersexplicit bounds

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Primes in congruence classes (11N13) Rate of growth of arithmetic functions (11N56) Analytic computations (11Y35)

Related Items (12)

On multiplicative functions with \(f(p+q+n_{0})=f(p)+f(q)+f(n_{0})\) ⋮ Parity of the coefficients of modular forms ⋮ Sieve methods for odd perfect numbers ⋮ On the products \((1^\ell + 1)(2^\ell + 1)\cdots(n^\ell + 1)\). II ⋮ Explicit Estimates: From Λ(n) in Arithmetic Progressions to Λ(n)/n ⋮ On the use of the least common multiple to build a prime-generating recurrence ⋮ A characterization of the identity with functional equations. II ⋮ On the divisibility of odd perfect numbers, quasiperfect numbers and amicable numbers by a high power of a prime ⋮ Medium-sized values for the prime number theorem for primes in arithmetic progressions ⋮ An improvement on the perfect order subsets of finite groups ⋮ Every odd number greater than $1$ is the sum of at most five primes ⋮ Quasiperfect numbers with the same exponent

Cites Work

• Explicit zero-free regions for Dirichlet L-functions
• Approximate formulas for some functions of prime numbers
• Explicit Estimates for θ (x; 3, l) and ψ(x; 3, l)
• On the Zeros of the Riemann Zeta Function in the Critical Strip. IV
• Primes in arithmetic progressions
• Explicit Bounds for Some Functions of Prime Numbers

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