Results 231 to 240 of about 4,959 (254)
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1980
We shall now deduce, from the results of the last section and those of §13, that $$\psi (x) = x + 0\left\{ {x\exp {{\left[ {\log x} \right]}^{\frac{1}{2}}}} \right\}$$ (1) and from this the analogous result for π(x), which includes the prime number theorem.
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We shall now deduce, from the results of the last section and those of §13, that $$\psi (x) = x + 0\left\{ {x\exp {{\left[ {\log x} \right]}^{\frac{1}{2}}}} \right\}$$ (1) and from this the analogous result for π(x), which includes the prime number theorem.
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1968
We have seen in the preceding chapter that Dirichlet’s L-functions have the property that L(1,χ)≠0 for χ ≠ χ1, and used it to show that every arithmetical progression of the form a + mk, where m>0, (a,m)=1, and k = 1,2,…, contains infinitely many primes.
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We have seen in the preceding chapter that Dirichlet’s L-functions have the property that L(1,χ)≠0 for χ ≠ χ1, and used it to show that every arithmetical progression of the form a + mk, where m>0, (a,m)=1, and k = 1,2,…, contains infinitely many primes.
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1971
This chapter discusses the prime number theorem. The subject of analytic number theory consists of the application of complex variable methods to the theory of numbers. The chapter discusses a connection between the Riemann zeta function and the properties of the prime numbers by means of the function L .
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This chapter discusses the prime number theorem. The subject of analytic number theory consists of the application of complex variable methods to the theory of numbers. The chapter discusses a connection between the Riemann zeta function and the properties of the prime numbers by means of the function L .
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2000
The last twenty years of the nineteenth century witnessed a rapid progress in the theory of complex functions, summed up in the monumental treatises of Emile Picard1 (1891–1896) and Camille Jordan2(1893–1896). The development of the theory of integral functions, started by Karl Weierstrass (1876) and rounded up by Jacques Hadamard (1893), revived the ...
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The last twenty years of the nineteenth century witnessed a rapid progress in the theory of complex functions, summed up in the monumental treatises of Emile Picard1 (1891–1896) and Camille Jordan2(1893–1896). The development of the theory of integral functions, started by Karl Weierstrass (1876) and rounded up by Jacques Hadamard (1893), revived the ...
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Generalizations of the Erdős–Kac Theorem and the Prime Number Theorem
Communications in Mathematics and Statistics, 2023Biao Wang, Zhining Wei
exaly
Some explicit estimates for the error term in the prime number theorem
Journal of Mathematical Analysis and Applications, 2023Daniel Johnston, Andrew Yang
exaly
2001
Let π(x) denote the number of primes p ≤ x. The prime number theorem is the assertion that $$ \mathop {\lim }\limits_{x \to \infty } \frac{{\pi (x)}} {{x/\log x}} = 1$$ .
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Let π(x) denote the number of primes p ≤ x. The prime number theorem is the assertion that $$ \mathop {\lim }\limits_{x \to \infty } \frac{{\pi (x)}} {{x/\log x}} = 1$$ .
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Analogues of the Prime Number Theorem and Mertens’ Theorem for Closed Orbits of the Motzkin Shift
Bulletin of the Malaysian Mathematical Sciences Society, 2015Habibulla Akhadkulov +2 more
exaly
Gallagherian Prime Geodesic Theorem in Higher Dimensions
Bulletin of the Malaysian Mathematical Sciences Society, 2019Muharem Avdispahić, Zenan Šabanac
exaly