@article{riemann1859, author = {Riemann, Bernhard}, title = {{\"U}ber die Anzahl der Primzahlen unter einer gegebenen Gr{\"o}sse}, journal = {Monatsberichte der K{\"o}niglichen Preu{\ss}ischen Akademie der Wissenschaften zu Berlin}, year = {1859}, pages = {671--680} } @book{abramowitz, author = {Abramowitz, Milton and Stegun, Irene A.}, title = {Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables}, publisher = {National Bureau of Standards}, series = {Applied Mathematics Series}, volume = {55}, address = {Washington, D.C.}, year = {1964} } @book{dingle, author = {Dingle, Robert Byron}, title = {Asymptotic Expansions: Their Derivation and Interpretation}, publisher = {Academic Press}, address = {London-New York}, year = {1973} } @article{lagarias, author = {Lagarias, Jeffrey C.}, title = {An Elementary Problem Equivalent to the Riemann Hypothesis}, journal = {The American Mathematical Monthly}, volume = {109}, number = {6}, pages = {534--543}, year = {2002} } @article{robin, author = {Robin, Guy}, title = {Grandes valeurs de la fonction somme des diviseurs et hypoth{\`e}se de Riemann}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, volume = {63}, number = {2}, pages = {187--213}, year = {1984} } @misc{espinosa-part1, author = {Espinosa, José Damián}, title = {A Beautiful Equivalence of the Riemann Hypothesis (The Riemann Hypothesis and Young's Lattice [Part 1/9])}, howpublished = {Zenodo preprint}, year = {2025}, month = dec, doi = {10.5281/zenodo.18251515}, url = {https://zenodo.org/records/18251515} } @misc{espinosa-part2, author = {Espinosa, José Damián}, title = {On a Theorem of Equivalences of the Riemann Hypothesis (The Riemann Hypothesis and Young's Lattice [Part 2/9])}, howpublished = {Zenodo preprint}, year = {2025}, month = dec, doi = {10.5281/zenodo.17834714}, url = {https://zenodo.org/records/17834714} } @misc{espinosa-part3, author = {Espinosa, José Damián}, title = {Two $\mathfrak{T}(k)$-Integral Equivalences of the Riemann Hypothesis (The Riemann Hypothesis and Young's Lattice [Part 3/9])}, howpublished = {Zenodo preprint}, year = {2025}, month = dec, doi = {10.5281/zenodo.17850259}, url = {https://zenodo.org/records/17850259} } @misc{espinosa-part4, author = {Espinosa, José Damián}, title = {Two $\mathfrak{T}(k)$-Summation Equivalences of the Riemann Hypothesis (The Riemann Hypothesis and Young's Lattice [Part 4/9])}, howpublished = {Zenodo preprint}, year = {2025}, month = dec, doi = {10.5281/zenodo.17923006}, url = {https://zenodo.org/records/17923006} } @misc{espinosa-part5, author = {Espinosa, José Damián}, title = {Five Equivalences of the Riemann Hypothesis (The Riemann Hypothesis and Young's Lattice [Part 5/9])}, howpublished = {Zenodo preprint}, year = {2025}, month = dec, doi = {10.5281/zenodo.17940307}, url = {https://zenodo.org/records/17940307} } @misc{espinosa-part6, author = {Espinosa, José Damián}, title = {On the Generalized Harmonic Number of a Partition $\boldsymbol{\lambda}$ and a $k$-tuple $\lambda$ (The Riemann Hypothesis and Young's Lattice [Part 6/9])}, howpublished = {Zenodo preprint}, year = {2025}, month = dec, doi = {10.5281/zenodo.18004964}, url = {https://zenodo.org/records/18004964} } @misc{espinosa-part7, author = {Espinosa, José Damián}, title = {The Assembly Theorem (The Riemann Hypothesis and Young's Lattice [Part 7/9])}, howpublished = {Zenodo preprint}, year = {2026}, month = jan, doi = {10.5281/zenodo.18121760}, url = {https://zenodo.org/records/18121760} } @misc{espinosa-part8a, author = {Espinosa, José Damián}, title = {My Path Toward the Proof of the Riemann Hypothesis (The Riemann Hypothesis and Young's Lattice [Part 8a/9])}, howpublished = {Zenodo preprint}, year = {2026}, month = jun, doi = {10.5281/zenodo.20685223}, url = {https://zenodo.org/records/20685223} } @misc{espinosa-part8b, author = {Espinosa, José Damián}, title = {The Riemann Hypothesis Young's Lattice Equivalence (The Riemann Hypothesis and Young's Lattice [Part 8b/9])}, howpublished = {Zenodo preprint}, year = {2026}, month = jun, doi = {10.5281/zenodo.20704552}, url = {https://zenodo.org/records/20704552} } @misc{espinosa-part8c, author = {Espinosa, José Damián}, title = {The Generalized Assembly Theorem (The Riemann Hypothesis and Young's Lattice [Part 8c/9])}, howpublished = {Zenodo preprint}, year = {2026}, month = jul, doi = {10.5281/zenodo.21325910}, url = {https://zenodo.org/records/21325910} } @book{stanley-ec1, author = {Stanley, Richard P.}, title = {Enumerative Combinatorics}, volume = {1}, edition = {2}, publisher = {Cambridge University Press}, series = {Cambridge Studies in Advanced Mathematics}, year = {2012} } @book{hardy1949divergent, author = {Hardy, G. 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