6 papers
Lambert -function and Gauss class number one conjecture
Igor V. Nikolaev
We study fixed points of a function arising in a representation theory of the Drinfeld modules by the bounded linear operators on a Hilbert space. We prove that such points corresp…
Quantum arithmetic of Drinfeld modules
Igor V. Nikolaev
We study the quantum invariants of projective varieties over the number fields. Namely, explicit formulas for a functor on such varieties are proved. The case of abel…
Addendum to "Measured foliations and Hilbert 12th problem"
Igor V. Nikolaev
We study numerical examples of the abelian extensions of the real quadratic number fields based on the results in Acta Mathematica Vietnamica 48 (2023), 271-281 (arXiv:0804.0057)
K-theory of Minkowski question-mark function
Igor V. Nikolaev
It is proved that the Minkowski question-mark function comes from the K-theory of Cuntz-Pimsner algebras. We apply this result to calculate the action of Frobenius endomorphism at…
Remark on height functions
Igor V. Nikolaev
Let be a number field and an -dimensional projective variety over . We use the -theory of a -algebra associated to to define a height of point…
Local factors and Cuntz-Pimsner algebras
Igor V. Nikolaev
We recast the local factors of the Hasse-Weil zeta function at infinity in terms of the Cuntz-Pimsner algebras. The nature of such factors is an open problem studied by Deninger an…