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This conjecture has been unsolved for over 160 years Revolutionary Breakthroughs in Number Theory, Complex Analysis, and the Riemann Hypothesis, shattering the Foundations of Mathematics, Breaking the Boundaries of Infinity In this revolutionary work, we demolish long-standing mathematical barriers and reconstruct the very fabric of number theory, complex analysis, and infinity itself. The old mathematical world is gone. Welcome to the new. I present an entirely original mathematical framework that overturns conventional understanding of numbers, infinity, and complex analysis. Through groundbreaking definitions and proofs, this work achieves what was previously deemed impossible: The Collapse of Infinite Products – Demonstrating that any non-unit complex number (S ≠ ±1), when multiplied by itself infinitely, converges to zero S*S*S*……. = 0 like : 5*5*5*…… =0 This research overturns centuries of mathematical consensus by proving that the Riemann zeta function at s =1 converges to an exact finite value Z(1) = ∏ 2/6 +1/12 We resolve one of the most counterintuitive problems in analytic number theory by proving the exact evaluation of the infinite product of negative primes: The Emptiness Paradigm : A Radical Reconstruction of the Complex Plane This work overturns 200 years of complex analysis by demonstrating the fundamental incompleteness of the Argand plane. We introduce new complex plane with emptiness space that looks like black hole In this proof that contains 294 pages, I will prove the conjecture of Riemann hypothesis using theorems and formulas that have never discovered before , I will also prove that there is and other function that is similar to Riemann Zeta Function and all its non trivial zeros lie exactly on critical strip – 1/2 If mathematician like Ramanujan has found the sum of this infinite series : 1+2+3+4+5+6+7+…… = -1/12 , I will prove the value of this infinite product : (-2)*(-3)*(-5)*(-7)*(-11)*(-13)*(-17)*…………. = ? If the mathematician Euler has prove that 1/12 +1/22 +1/32 +1/42 +1/52 +….. =∏ 2/6 In this proof , I will generalize this formula for any S , hence S is a complex number Z(S) + Z(-S) = ∏ 2/6 You will find many other formulas and theorems that justify and prove Riemann hypothesis conjecture
bouazad E. 2025. Riemann Hypothesis Last Version. PREPRINTS.RU. https://doi.org/10.24108/preprints-3113574