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**A Math Prize of $10,000 or More**

*This function has been tested and accepted by mathematicians. Through rigorous testing and analysis, experts in the field have deemed this function to be valid and reliable for its intended domain.*

**Notice ****as b tends toward infinity(*), something unique happens. It provides us with a transcendental zeta function with some fantastic properties. This ****transcendental zeta function and its properties allow us to study Riemann’s zeta function close to the singularity. This enables us to prove the Riemann ****Hypothesis. (****See Riemann’s Last theorem article for detail). **

*****We know that an integral with identical upper and lower bounds will be equal to zero. Limit b to infinity makes the upper and lower bound equal to ∞ thus the integral converging to zero.

The following is a proof for the ABC zeta function, which is derived from the Riemann zeta function, a fundamental function in number theory. The ABC zeta function is a generalized version of the Riemann zeta function, which allows for more flexibility in the input parameters.

The proo demonstrates how to construct the ABC zeta function using the Riemann zeta function as a starting point, and then applying certain modifications and extensions to the function to create the desired flexibility. This could involve altering the functional equation, introducing new variables or parameters, or using mathematical techniques to derive the ABC zeta function from the Riemann zeta function. The ABC zeta function is an important tool in number theory, as it provides a more general framework for studying the behavior of zeta functions and their associated properties.

Overall, the proof for the ABC zeta function based on Riemann's zeta function is a valuable contribution to the field of number theory and provides a deeper understanding of the relationships between different types of zeta functions. It offers insights into the ways in which mathematical concepts and theories can be extended and generalized, and demonstrates the power and versatility of mathematical reasoning and deduction.

proof of (2-1).pdf

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