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Can anyone suggest me a very useful book which contains the following:

-Dirichlet series and Riemann Zeta Function. Möbius function, von Mangoldt function and Möbius inversion formula.

-Important Dirichlet series and arithmetic functions.

-Meromorphic continuation of Riemann Zeta Function.

-Entire functions, entire function's series, meromorphic function's series and Hadamard's factorization theorem.

-Zeroes of Riemann Zeta Function and factorization formula. Hamburger's inversion theorem.

-Theorem of Hadamard and de la Vallee Poussin.

-Prime numbers theorem.

-Riemann hypothesis and its consequences.

-Finite Abelian groups and its characters.

-Dirichlet's characters. Gaussian sums.

-Dirichlet L-function.

-Dirichlet's prime number theorem in arithmetic progressions.

-Distribution of prime numbers in arithmetic progressions.

Of course, if there is more then one book, you are very welcome to submit it.

Thanks in advance!

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  • 2
    $\begingroup$ You might try any introductory analytic number theory text and find all of this, or most of this with references to the rest. Typical classics include Apostol's Intro to Analytic NT, Davenports Multiplicative NT, or Montogomery and Vaughan's number theory book. As an aside: It's probably reasonable to close this question as a duplicate of questions asking for introductory resources on analytic number theory. $\endgroup$ – davidlowryduda Sep 21 '17 at 14:49
  • $\begingroup$ Try apostol and Iwaniec $\endgroup$ – reuns Sep 22 '17 at 7:07

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