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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Research Questions
1.4 Objectives of the Study
1.5 Significance of the Study
1.6 Limitations of the Study
1.7 Scope of the Study

Chapter 2: Literature Review
2.1 Analytic Number Theory
2.2 Selberg Sieve
2.3 Previous Studies on Analytic Number Theory and Selberg Sieve
2.4 Gaps in the Literature

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection
3.3 Data Analysis
3.4 Selection of Participants
3.5 Ethical Considerations

Chapter 4: Discussion of Findings
4.1 Analysis of Data
4.2 Interpretation of Results
4.3 Comparison with Previous Studies
4.4 Implications of Findings

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Recommendations for Future Research
5.4 Contribution to the Field

Brief Overview on Analytic Number Theory and Selberg Sieve:

Analytic number theory is a branch of mathematics that deals with the properties of integers and their relationships with other mathematical objects. It involves the use of techniques from analysis, such as calculus and complex analysis, to study the distribution of prime numbers and other arithmetical objects.

Selberg sieve is a method developed by the Norwegian mathematician Atle Selberg for sieving out integers that satisfy certain properties. It is used in number theory to study the distribution of prime numbers and to prove results related to prime numbers, such as the prime number theorem.

In this thesis, the researcher aims to explore the connections between analytic number theory and Selberg sieve, and to investigate how the techniques from these two areas can be used together to solve problems in number theory. The study will involve a detailed literature review of previous research in this area, as well as the development of a research methodology to analyze the data and draw meaningful conclusions. The findings of the study will be discussed in chapter four, followed by a conclusion and summary in chapter five.

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