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math.NT2026
A note on Shintani's invariants
Bora Yalkinoglu
Shintani's celebrated invariants are conjectured to generate abelian extensions of real quadratic number fields, offering a potential solution to Hilbert's 12th problem in that set…
math.NT2025
Shintani's invariant via cyclic quantum dilogarithm
Bora Yalkinoglu
We formulate Shintani's invariant in terms of the cyclic quantum dilogarithm. Building on earlier results that expressed Shintani's invariant using the -Pochhammer symbol, we sh…
math.NT2025
Bost-Connes systems and periodic Witt vectors
Bora Yalkinoglu
In this note, using Borger's theory of periodic Witt vectors, we construct integral refinements of the arithmetic subalgebras associated with Bost-Connes systems for general number…