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NUMBER THEORY (M2,Davenport)

Lecture Topic : (Math Physics) NUMBER THEORY (M2, Davenport)

Prerequisites :

Recommended Text(s) :

“Multiplicative Number Theory”, 2nd Edn., Graduate Texts in Mathematics (GTM) No. 50, Harold M. Edwards, Springer, 1974.

Approx price new on Amazon.com (hard copy) : $56

Approx price second hand on Amazon.com (hard copy) : $51

Availability free on eMule.com (e-format) : Yes

eMule search key word(s) :Davenport, Multiplicative Number Theory

Lectures and Links :

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Lecture 1  (link)

Ch.1   Primes in Arithmetic Progression

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Lecture 2  (link)

Ch.2   Gauss’s Sum

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Lecture 3  (link)

Ch.3   Cyclotomy

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Lecture 4 (link)

Ch.4   Primes in Arithmetic Progression : The General Modulus

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Lecture 5  (link)

Ch.5   Primitive Characters

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Lecture 6  (link)

Ch.6   Dirichlet’s Class Number Formula

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Lecture 7  (link)

Ch.7   The Distribution of the Primes

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Lecture 8  (link)

Ch.8   Riemann’s Memoir

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Lecture 9  (link)

Ch.9   The Functional Equation of the L Functions

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Lecture 10  (link)

Ch.10   Properties of the G Function

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Lecture 11  (link)

Ch.11   Integral Functions of Order 1

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Lecture 12  (link)

Ch.12   The Infinite Products for x(s) and x(s, c)

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Lecture 13  (link)

Ch.13   A Zero-Free Region for z(s)

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Lecture 14  (link)

Ch.14   Zero-Free Regions for L(s, c)

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Lecture 15  (link)

Ch.15   The Number N(T)

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Lecture 16  (link)

Ch.16   The Number N(T,c)

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Lecture 17  (link)

Ch.17   The Explicit Formula for y (x)

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Lecture 18  (link)

Ch.18   The Prime Number Theorem

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Lecture 19  (link)

Ch.19   The Explicit Formula for y (x, c)

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Lecture 20  (link)

Ch.20   The Prime Number Theorem for Arithmetic Progressions 1

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Lecture 21  (link)

Ch.21   Siegel’s Theorem

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Lecture 22  (link)

Ch.22   The Prime Number Theorem for Arithmetic Progressions 2

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Lecture 23  (link)

Ch.23   The Polya-Vinogradov Inequality

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Lecture 24  (link)

Ch.24   Further Prime Number Sums

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Lecture 25  (link)

Ch.25   An Exponential Sum Formed with Primes

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Lecture 26  (link)

Ch.26   Sums of Three Primes

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Lecture 27  (link)

Ch.27   The Large Sieve

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Lecture 28  (link)

Ch.28   Bombieri’s Theorem

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Lecture 29  (link)

Ch.29   An Average Result

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Lecture 30  (link)

Ch.30   References to Other Work

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