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A Generalisation of Niven's Theorem for Trigonometric Functions
Adam Keilthy, Ailbhe Ní Ruairí
Niven's Theorem asserts that . This paper uses elementary methods to classify all elements in the sets $\…
Formal deformations of modular forms and multiple L-values
Adam Keilthy, Martin Raum
We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leverag…
Evaluation of the multiple zeta values and period polynomial relations
Steven Charlton, Adam Keilthy
In studying the depth filtration on multiple zeta values, difficulties quickly arise due to a disparity between it and the coradical filtration. In particular, there are additional…
A generalisation of quasi-shuffle algebras and an application to multiple zeta values
Adam Keilthy
A large family of relations among multiple zeta values may be described using the combinatorics of shuffle and quasi-shuffle algebras. While the structure of shuffle algebras have…
Motivic Multiple Zeta Values and the Block Filtration
Adam Keilthy
We extend the block filtration, defined by Brown based on the work of Charlton, to all motivic multiple zeta values, and study relations compatible with this filtration. We constru…