4 papers
Arithmetic aspects of discrete periodic Toda flows
Bora Yalkinoglu
We construct a new algebraic linearization of the discrete periodic Toda flow by using Mumford's algebraic description of the Jacobian of a hyperelliptic curve. In particular, the…
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…
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…
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…