Good theory in number theory for deep understanding

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SUMMARY

The discussion centers on the search for a comprehensive book on number theory that provides deep theoretical understanding, similar to the works of Kiselev in geometry and Apostol in calculus. Participants recommend "Apostol's Number Theory" as a masterpiece and suggest "An Introduction to the Theory of Numbers" by I. Niven and H. S. Zuckerman, although it lacks depth in theoretical explanations. Additionally, "Ireland and Rosen" and "Davenport's Multiplicative Number Theory" are highlighted as essential texts for a solid foundation in number theory.

PREREQUISITES
  • Understanding of basic number theory concepts
  • Familiarity with mathematical proofs and problem-solving techniques
  • Knowledge of modular forms and Dirichlet series
  • Experience with calculus, particularly Apostol's methods
NEXT STEPS
  • Research "Apostol's Number Theory" for comprehensive theoretical insights
  • Explore "Ireland and Rosen" for foundational concepts in number theory
  • Study "Davenport's Multiplicative Number Theory" for advanced topics
  • Investigate modular forms and Dirichlet series for deeper mathematical applications
USEFUL FOR

Mathematicians, students of number theory, and educators seeking in-depth theoretical resources to enhance their understanding of number theory concepts.

simpy
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Does anybody of a good book in number theory for deep understanding of concepts like kiselev in geometry and apostol in calculus ? I have 'introduction to theory of numbers' by I. Niven and H. S. Zuckerman but I feel it is not suitable for my purpose , there is no description of 'why we did this' in the book and in examples too the book does not encourage the reader to solve the problem on his/her own.
All I mean by above is that although the questions' quality is good in the book but theory is not and I need a good theory book.
So, if you know any book that can meet my purpose, share it here.
 
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Apostol's Number Theory book is a masterpiece ..
The follow-up on Modular forms and Dirichlet series .. is also a masterpiece.
Wakabaloola
 
Well there's the classic text by Ireland and Rosen, I think this book alongside Davenport's Multiplicative Number theory is a good start in theory respect.
 

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