On the Riemann Hypothesis and its generalizations

A proof for the original Riemann hypothesis is proposed based on the infinite Hadamard product representation for the Riemann zeta function and later generalized to Dirichlet L-functions. The extension of the hypothesis to other functions is also discussed.

💡 Research Summary

The manuscript titled “On the Riemann Hypothesis and its Generalizations” attempts to prove the classical Riemann Hypothesis (RH) by exploiting the infinite Hadamard product representation of the Riemann zeta function, and then extends the argument to Dirichlet L‑functions (the Generalized Riemann Hypothesis, GRH) and to Dedekind zeta functions (the Extended Riemann Hypothesis, ERH).

Outline of the Proposed Proof

1. The author introduces the symmetric function
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