Apostol, Tom M. Introduction to Analytic Number Theory. Springer-Verlag, New York, 1976.
I have completed the first three chapters and am done with the majority of the problems in chapter four. The solutions are in a pdf document that is constantly being updated. I have broken up the document into individual chapters below. The following are all in pdf format.
- Chapter 1: The Fundamental Theorem of Arithmetic (All)
- Chapter 2: Arithmetical Functions and Dirichlet Convolution (All)
- Chapter 3: Averages of Arithmetical Functions (All)
- Chapter 4: Some Elementary Theorems on the Distribution of Prime Numbers (21/30)
Van Lint and Wilson. A Course in Combinatorics (Second Edition). Cambridge University Press, 2001.
Edit: People have been using the solutions to copy them down for assignments rather than to learn from them. As a result, I’m taking them down, at least for now.
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I have looked into your solutions – still am in fact- and have helped me a lot in my studies thanks.
Cannot wait to look at the other chapters 🙂
I need the rest of the chapters 😦 😦 😦
😦
I need the rest of the chapters 😦 😦 😦 of Introduction to Analytic Number Theory
Sorry, I don’t have them!
For question 1 part (b) in chapter 4, I believe the solution is 9*49 = 21*21 = 441, not 693.
Yes, thanks for catching that! I have updated the solutions.
No problems (it’s a mere blemish on your solutions; really nice work). I too am self studying this book and your solutions have been helpful.
Thanks! I just finished chapter 4 too and have worked through most of the problems. Keep working through the book and updating your solutions!
Dear Mr. Biel & Sean Li, I’m working on my own on Apostol & finished all problems for Ch. 4 except the very last, 30.(b). Can you give any hints? It sounds like just rearranging inequality expressions to arrive at his final: alpha*gamma <= alpha <= beta <= alpha*delta.
When I took his 2 inequalities from 30.(a) & also alpha<=beta from 28., it doesn't seem to follow?
It helped in me a lot specially in preparing my assignment ..Thanks . But I need solution of chapter 5 also. Kindly, provide it if possible.
second chapter answers
i want combinatorics solution tomorrow is my exam pls provide me as soon as possible
Answer to question 12.22 part c) has errors.
I) The “proof” states that
K^(1-sigma)/(1-sigma) <= K^(1/log(K))/(1 / log(K)) = e log(K)
which implies that 1/(1-sigma) = 1 – 1/log(K)