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Mikuláš Zindulka

Hi! I'm a Ph.D. student at the Charles University in Prague. I work in the number theory group led by my advisor Víťa Kala.

Research

I'm interested in both algebraic and analytic number theory. My research interests include:

  • Hurwitz class numbers, families of elliptic curves, and applications of modular forms in number theory
  • Arithmetics of number fields
  • Theory of partitions
  • Questions related to Artin's conjecture for primitive roots
  • Lattice models in combinatorics

Contact

mikulas.zindulka@matfyz.cuni.cz

Papers

Totally positive elements with m partitions exist in almost all real quadratic fields, preprint on arXiv, September 2024

(with O. Chwiedziuk, M. Doležálek, S. Hlavinková, E. Pěchoučková, Z. Pezlar, O. Prakash, and A. Růžičková) No proper generalized quadratic forms are universal over quadratic fields, preprint on arXiv, September 2024

Sums of Hurwitz class numbers, CM modular forms, and primes of the form x^2+ny^2, preprint on arXiv, May 2024

(with O. Chwiedziuk, M. Doležálek, E. Pěchoučková, Z. Pezlar, O. Prakash, G. Romeo, and A. Růžičková) Representing rational integers by generalized quadratic forms over quadratic fields, preprint on arXiv, March 2024

(with M. Doležálek, M. Raška, E. Sgallová, and E. N. Stucky) The Six-Vertex Model with a Non-Standard Boundary Condition, preprint on arXiv, October 2023

(with D. Stern) Partitions in real quadratic fields, Mathematische Nachrichten, published online, November 2024

(with V. Kala) Partitions into powers of an algebraic number, The Ramanujan Journal, Vol. 64, April 2024

(with M. Tinková and E. Waxman) Artin Twin Primes, Journal of Number Theory, Vol. 245, April 2023