in arithmetic progressions
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4 matching pages
1: 27.11 Asymptotic Formulas: Partial Sums
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►where , .
►Letting
in (27.11.9) or in (27.11.11) we see that there are infinitely many primes if are coprime; this is Dirichlet’s theorem
on primes in arithmetic progressions.
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►The prime number theorem for
arithmetic progressions—an extension of (27.2.3) and first proved in de la Vallée Poussin (1896a, b)—states that if , then the number of primes with is asymptotic to as .
2: 25.15 Dirichlet -functions
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►This result plays an important role in the proof of Dirichlet’s theorem on primes in arithmetic progressions (§27.11).
Related results are:
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3: 1.2 Elementary Algebra
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Arithmetic Progression
… ►Geometric Progression
… ►§1.2(iv) Means
►The arithmetic mean of numbers is … ►Linear Equations in Unknowns
…4: Bibliography K
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Heat conduction and diffusion in a fluid medium with a periodic flow. I. Determination of the wave transfer coefficient in a tube, slot, and canal.
Akad. Nauk SSSR. Žurnal Eksper. Teoret. Fiz. 21, pp. 964–978.
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Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 module for an interval data type.
ACM Trans. Math. Software 22 (4), pp. 385–392.
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Algorithm 910: a portable C++ multiple-precision system for special-function calculations.
ACM Trans. Math. Software 37 (4), pp. Art. 45, 27.
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Two new asymptotic methods in the theory of wave propagation in inhomogeneous media.
Sov. Phys. Acoust. 14, pp. 1–17.
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Rays and caustics as physical objects.
In Progress in Optics, E. Wolf (Ed.),
Vol. 26, pp. 227–348.
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