Prime Numbers and Indian Contributions to Analytic Number Theory
Abstract: Prime numbers have long been central to the development of number theory, forming the building blocks of arithmetic. Analytic number theory, a branch that uses tools from mathematical analysis to study integers and prime distributions, has evolved through contributions from mathematicians across the globe. Among these, Indian mathematicians- most notably Srinivasa Ramanujan- have played a transformative role. This paper explores the theory of prime numbers, the foundations of analytic number theory, and highlights major Indian contributions, particularly focusing on Ramanujan?s work and its continuing impact. The study also briefly discusses earlier Indian mathematical traditions and modern developments influenced by Indian scholars.
Keywords: Prime Numbers, Analytic Number Theory, Prime Number Theorem, Riemann Zeta Function, Ramanujan Primes, Partition Function, Hardy?Ramanujan Formula, Modular Forms
How to Cite?: Amit Kumar Alok, "Prime Numbers and Indian Contributions to Analytic Number Theory", Volume 15 Issue 3, March 2026, International Journal of Science and Research (IJSR), Pages: 1746-1748, https://www.ijsr.net/getabstract.php?paperid=SR26329215037, DOI: https://dx.doi.org/10.21275/SR26329215037