Prime Sine Function and The Riemann Hypothesis

This book's fundamental aim is to explore and affirm the following proposition: the sums of the reciprocal powers of the zeros of any entire function serve as the "genetic codes" that determine the behavior of the function. This central concept provides a basis for the construction of various fascinating functions. I will illustrate how this principle is utilized to devise unique functions such as the Prime Sine function, the Prime Gamma function, and the Twin Primes function, all of which have zeros at prime numbers and twin primes. The possibilities are truly infinite.Consequently, this fresh viewpoint simplifies numerous proofs, making them more accessible to a wider audience. It enables the creation of new functions based on predetermined zeros. By applying this idea, I have uncovered and defined the prime sine function, characterized by its zeros at prime numbers. This innovative perspective offers a fresh avenue to explore prime numbers and the Riemann Hypothesis, leading to fascinating findings detailed in this book.