F. Gawron

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20212026

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math.NT2026

Congruences and ramified primes in fields of coefficients of newforms

Nuno Freitas, Filip Gawron

We investigate the splitting behavior of $ℓ$ in the coefficient field of a newform $f$ of level $N$ , under the assumption that $f$ is congruent modulo a prime above $ℓ$ to an…

math.NT2024

Signs behaviour of sums of weighted numbers of compositions

Filip Gawron, Maciej Ulas

Let $A$ be a subset of positive integers. For a given positive integer $n$ and $0 \leq i \leq n$ let $c_{A} (i, n)$ denotes the number of $A$ -compositions of $n$ with exactly $i$ parts…

math.NT2022

Signs behaviour of sums of weighted numbers of partitions

Filip Gawron, Maciej Ulas

Let $A$ be a subset of positive integers. By $A$ -partition of $n$ we understand the representation of $n$ as a sum of elements from the set $A$ . For given $i, n \in N$ , by $c_{A}(i,…

math.NT2021

On length of the period of the continued fraction of $n d$

Filip Gawron, Tomasz Kobos

For a given quadratic irrational $α$ , let us denote by $D (α)$ the length of the periodic part of the continued fraction expansion of $α$ . We prove that for a positive integer $d$ ,…

Congruences and ramified primes in fields of coefficients of newforms

Signs behaviour of sums of weighted numbers of compositions

Signs behaviour of sums of weighted numbers of partitions

On length of the period of the continued fraction of nd​

On length of the period of the continued fraction of $n d$