Zafer Selcuk Aygin

activity

20162021

collaborators

7 papers

math.NT2021

Sums of triangular numbers and sums of squares

Amir Akbary, Zafer Selcuk Aygin

For non-negative integers $a, b,$ and $n$ , let $N (a, b; n)$ be the number of representations of $n$ as a sum of squares with coefficients $1$ or $3$ ( $a$ of ones and $b$ of threes).…

math.NT2021

N-colored generalized Frobenius partitions: Generalized Kolitsch identities

Zafer Selcuk Aygin, Khoa D. Nguyen

Let $N \geq 1$ be squarefree with $(N, 6) = 1$ . Let $c ϕ_{N} (n)$ denote the number of $N$ -colored generalized Frobenius partition of $n$ introduced by Andrews in 1984. We prove $$ cϕ_N(n)…

math.NT2021

Projections of modular forms on Eisenstein series and its application to Siegel's formula

Zafer Selcuk Aygin

Let $k \geq 2$ and $N$ be positive integers and let $χ$ be a Dirichlet character modulo $N$ . Let $f (z)$ be a modular form in $M_{k} (Γ_{0} (N), χ)$ . Then we have a unique decomposition $f…

math.NT2020

Monogenic pure cubics

Zafer Selcuk Aygin, Khoa D. Nguyen

Let $k \geq 2$ be a square-free integer. We prove that the number of square-free integers $m \in [1, N]$ such that $(k, m) = 1$ and $Q (3 k^{2} m)$ is monogenic is $\gg N^{1…

math.NT2018

Extensions of Ramanujan-Mordell formula with coefficients $1$ and $p$

Zafer Selcuk Aygin

We use properties of modular forms to prove the following extension of the Ramanujan-Mordell formula, \begin{align*} z^{k-j}z_p^{j}=&\frac{p_χ^{k-j}-1}{p_χ^{k}-1}F_p(k,j;τ)+ \frac{…

math.NT2017

Representations by sextenary quadratic forms with coefficients $1, 2, 3$ and $6$ and on newforms in $S_{3} (Γ_{0} (24), χ)$

Zafer Selcuk Aygin

We use theory of modular forms to give formulas for $N (1^{l_{1}}, 2^{l_{2}}, 3^{l_{3}}, 6^{l_{6}}; n)$ for all $l_{1}, l_{2}, l_{3}, l_{6} \in N_{0}$ , with $l_{1} + l_{2} + l_{3} + l_{6} = 6$ . We also apply our r…

Sums of triangular numbers and sums of squares

N-colored generalized Frobenius partitions: Generalized Kolitsch identities

Projections of modular forms on Eisenstein series and its application to Siegel's formula

Monogenic pure cubics

Extensions of Ramanujan-Mordell formula with coefficients 1 and p

Representations by sextenary quadratic forms with coefficients 1,2,3 and 6 and on newforms in S3​(Γ0​(24),χ)

Extensions of Ramanujan-Mordell formula with coefficients $1$ and $p$

Representations by sextenary quadratic forms with coefficients $1, 2, 3$ and $6$ and on newforms in $S_{3} (Γ_{0} (24), χ)$