Research
Research
Z. Masáková and M. Tinková, Finiteness in real cubic fields, Acta Math. Hungar. 153, (2017) 318-333.
M. Čech, D. Lachman, J. Svoboda, M. Tinková and K. Zemková, Universal quadratic forms and indecomposables over biquadratic fields, Math. Nachr. 292, (2019) 540-555.
M. Tinková and P. Voutier, Indecomposable integers in real quadratic fields, J. Number Theory 212, (2020) 458-482.
J. Krásenský, M. Tinková and K. Zemková, There are no universal ternary quadratic forms over biquadratic fields, Proc. Edinb. Math. Soc. 63 (3), (2020) 861-912.
M. Tinková, Arithmetics in number systems with cubic base, Publ. Math. Debrecen 99, (2021) 25-50.
B. Faye, L. Matthiesen, D. Schindler, M. Tinková and K. Zemková, Integers Represented by Ternary Quadratic Forms, Women in Numbers Europe III: Research Directions in Number Theory, Association for Women in Mathematics Series, vol 24, Springer, (2021) 207-231.
M. Tinková, E. Waxman and M. Zindulka, Artin twin primes, J. Number Theory 245, (2023) 203-232.
V. Kala and M. Tinková, Universal quadratic forms, small norms and traces in families of number fields, Int. Math. Res. Not. IMRN 2023, (2023) 7541-7577.
M. Tinková, Trace and norm of indecomposable integers in cubic orders, Ramanujan J. 61, (2023) 1121-1144.
M. Tinková, On the Pythagoras number of the simplest cubic fields, Acta Arith. 208, (2023) 325-354. codes
D. Gil Muñoz and M. Tinková, The lifting problem for universal quadratic forms over simplest cubic fields, Bull. Aust. Math. Soc. 110, (2024) 77-89.
D. Gil Muñoz and M. Tinková, Additive structure of non-monogenic simplest cubic fields, Ramanujan J. 66, (2025) 47. code
V. Kala, E. Sgallová and M. Tinková, Arithmetic of cubic number fields: Jacobi–Perron, Pythagoras, and indecomposables, J. Number Theory 273, (2025) 37-95. codes
M. Tinková, Bounds on the Pythagoras number and indecomposables in biquadratic fields, Proc. Edinb. Math. Soc. 68 (3), (2025) 843-868.
C. Frei and M. Tinková, Linear constellations in primes with arithmetic restrictions, submitted.
M. Tinková, R. Visser and P. Yatsyna, Sums of two units in number fields, submitted.
M. Tinková and P. Yatsyna, Additively indecomposable quadratic forms over totally real number fields, to appear in J. Lond. Math. Soc. codes
S. Fryšová and M. Tinková, Additively indecomposable quadratic forms over biquadratic and simplest cubic fields, submitted.
Units with Property (F) in cubic number fields, Combinatorial and Algebraic Structures Seminar, Prague, Czech Republic
Finiteness in real cubic fields, Combinatorics on Words 2017, Janov nad Nisou, Czech Republic
Finiteness in real cubic fields, Numeration 2017, Rome, Italy
Arithmetics in number systems with cubic base, Number Theory Seminar, Prague, Czech Republic
Indecomposable integers and universal quadratic forms, Numeration 2018, Paris, France
Indecomposable integers and universal quadratic forms, wds-m 2018, Prague, Czech Republic
Universal quadratic forms and indecomposables over biquadratic fields, Number Theory Seminar, Prague, Czech Republic
Universal quadratic forms and indecomposables over biquadratic fields, Combinatorics on Words 2018, Janov nad Nisou, Czech Republic
Arithmetics in number systems with cubic base, ALANT 5, Bedlewo, Poland
Greedy expansions and property (F), Autumn School of the Department of Algebra 2018, Rybniště, Czech Republic
Indecomposable integers in real quadratic fields of odd discriminant, Number Theory Seminar, Prague, Czech Republic
Jacobi-Perron algorithm and indecomposable integers in the simplest cubic fields, wds-m 2019, Prague, Czech Republic
Indecomposable integers in real quadratic fields, Combinatorics on Words 2019, Janov nad Nisou, Czech Republic
Jacobi-Perron algorithm and indecomposable integers in the simplest cubic fields, Numeration 2019, Vienna, Austria
Jacobi-Perron algorithm and indecomposable integers in the simplest cubic fields, 24th Central European Number Theory Conference, Komárno, Slovakia
Jacobi-Perron algorithm and indecomposable integers in the simplest cubic fields, Oberseminar Algebra und Geometrie, Dortmund, Germany
Universal quadratic forms, small norms and traces in families of number fields, Zahlentheoretisches Kolloquium, Graz, online
On the Pythagoras number of the simplest cubic fields, ALGAR 2021, Antwerp, Belgium
Universal quadratic forms, small norms and traces in families of number fields, One World Numeration Seminar, online
Trace and norm of indecomposable integers in cubic orders, Number Theory Conference 2022, Debrecen, Hungary
Universal quadratic forms, small norms and traces in families of number fields, ELAZ 2022, Poznań, Poland
Additive structure of non-monogenic simplest cubic fields, WINGs 2023, Chesterfield, United Kingdom
Additive structure of non-monogenic simplest cubic fields, Numeration 2023, Liège, Belgium
Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables, Zahlentheoretisches Kolloquium, Graz, Austria
Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables, Journées Arithmétiques 2023, Nancy, France
Additive structure of non-monogenic simplest cubic fields, 25th Central European Number Theory Conference, Sopron, Hungary
Trace and norm of indecomposable integers in cubic orders, Young Number Theorists in Bonn, Bonn, Germany
Bounds on the Pythagoras number and indecomposables in biquadratic fields, Dynamics and Number Theory, Krakow, Poland
Non-decomposable quadratic forms over totally real fields, Numeration 2024, Utrecht, Netherlands
Non-decomposable quadratic forms over totally real fields, ELAZ 2024, Rostock, Germany
Artin twin primes, SAAAJ-Seminar, Graz, Austria
Non-decomposable quadratic forms over totally real number fields, Number Theory Seminar, Prague, Czech Republic
Bounds on the Pythagoras number and indecomposables in biquadratic fields, Squares in Dortmund, Dortmund, Germany
Non-monogenic simplest cubic fields, Number Theory Seminar, Prague, Czech Republic
Non-decomposable quadratic forms over totally real number fields, Conference on the Arithmetic Theory of Quadratic Forms and Lattices, Seoul, South Korea
Non-decomposable quadratic forms over totally real number fields, Journées Arithmétiques 2025, Esch-sur-Alzette, Luxembourg
Non-decomposable quadratic forms over totally real number fields, 26th Central European Number Theory Conference, Salzburg, Austria
2nd French-German Summer School, Dresden, Germany
Women in Numbers Europe 3, Rennes, France
Front Range Number Theory Day, Spring 2021, online
ALGAR 2021, Antwerp, Belgium
Arithmetic Statistics and Local-Global Principles, Vienna, Austria
ALGAR 2022, Antwerp, Belgium
ALGAR 2023, Antwerp, Belgium
Principal investigator of GAUK grant Indecomposable integers and universal quadratic forms, 2018-2020 (with Martin Čech, Kristýna Zemková, Ester Sgallová and J. Krásenský)
Principal investigator of GAČR grant Local-global problems over number fields, 2022-2025 (Postdoc Individual Fellowship – Outgoing, including a stay in Graz for two years)