P'eter P. Varj'u

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math.NT2026

Lifting all elements in $SL_{n} (Z / q Z)$

Amitay Kamber, PÃ©ter P. VarjÃº

We show that every element of $SL_{n} (Z / q Z)$ can be lifted to an element of $SL_{n} (Z)$ of norm at most $C q^{2} lo g q$ , while there exist…

math.NT2026

Counting rationals and diophantine approximation in missing-digit Cantor sets

Sam Chow, PÃ©ter P. VarjÃº, Han Yu

We establish a new upper bound for the number of rationals up to a given height in a missing-digit set, making progress towards a conjecture of Broderick, Fishman, and Reich. This…

math.NT2025

A random polynomial with multiplicative coefficients is almost surely irreducible

Assume that the Riemann hypothesis holds for Dedekind zeta functions. Under this assumption, we prove that a degree $d$ polynomial with random multiplicative $\pm 1$ coefficients is…

Lifting all elements in SLn​(Z/qZ)

Counting rationals and diophantine approximation in missing-digit Cantor sets

A random polynomial with multiplicative coefficients is almost surely irreducible

Lifting all elements in $SL_{n} (Z / q Z)$