Zafer Selcuk Aygin

activity

20162023

M_{2 k} (Γ_{0} (N))

and their applications

6 citations · 12 across the 10 of their papers we have counts for

collaborators

12 papers

math.NT2023

Bounds for orders of zeros of a class of Eisenstein series and their applications on dual pairs of eta quotients

Amir Akbary, Zafer Selcuk Aygin

Let $k$ be an even positive integer, $p$ be a prime and $m$ be a nonnegative integer. We find an upper bound for orders of zeros (at cusps) of a linear combination of classical Eis…

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★ 3 cited

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…

math.NT2017★ 6 cited

On Eisenstein series in $M_{2 k} (Γ_{0} (N))$ and their applications

Zafer Selcuk Aygin

Let $k, N \in N$ with $N$ square-free and $k > 1$ . We prove an orthogonal relation and use this to compute the Fourier coefficients of the Eisenstein part of any $f(z) \in M_…

math.NT2016

Eisenstein Series and Convolution Sums

Zafer Selcuk Aygin

We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution…

math.NT2016

Theta Products and Eta Quotients of Level $24$ and Weight $2$

Ayşe Alaca, Şaban Alaca, Zafer Selcuk Aygin

We find bases for the spaces $M_{2} (Γ_{0} (24), (\frac{d}{\cdot}))$ ( $d = 1, 8, 12, 24$ ) of modular forms. We determine the Fourier coefficients of all $35$ theta products $φ…

math.NT2016★ 1 cited

Eta quotients, Eisenstein series and Elliptic Curves

Ayse Alaca, Saban Alaca, Zafer Selcuk Aygin

We express all the newforms of weight $2$ and levels $30$ , $33$ , $35$ , $38$ , $40$ , $42$ , $44$ , $45$ as linear combinations of eta quotients and Eisenstein series, and list their co…

math.NT2016★ 2 cited

A family of Eta Quotients and an Extension of the Ramanujan-Mordell Theorem

Ayse Alaca, Saban Alaca, Zafer Selcuk Aygin

Let $k \geq 2$ be an integer and $j$ an integer satisfying $1 \leq j \leq 4 k - 5$ . We define a family ${C_{j, k} (z)}_{1 \leq j \leq 4 k - 5}$ of eta quotients, and prove that this fami…

Bounds for orders of zeros of a class of Eisenstein series and their applications on dual pairs of eta quotients

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)

On Eisenstein series in M2k​(Γ0​(N)) and their applications

Eisenstein Series and Convolution Sums

Theta Products and Eta Quotients of Level 24 and Weight 2

Eta quotients, Eisenstein series and Elliptic Curves

A family of Eta Quotients and an Extension of the Ramanujan-Mordell Theorem

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 $S_{3} (Γ_{0} (24), χ)$

On Eisenstein series in $M_{2 k} (Γ_{0} (N))$ and their applications

Theta Products and Eta Quotients of Level $24$ and Weight $2$