Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Aygin, Zafer Selcuk"'
Autor:
Akbary, Amir, Aygin, Zafer Selcuk
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 Eisenstein series of weight $k$ and level $p^m$. As an immediate conseque
Externí odkaz:
http://arxiv.org/abs/2306.10218
Autor:
Akbary, Amir, Aygin, Zafer Selcuk
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). Let $N^*(a,b; n)$ be the number of representations of $n$ as a sum of
Externí odkaz:
http://arxiv.org/abs/2107.00787
Autor:
Aygin, Zafer Selcuk, Nguyen, Khoa D.
Let $N\geq 1$ be squarefree with $(N,6)=1$. Let $c\phi_N(n)$ denote the number of $N$-colored generalized Frobenius partition of $n$ introduced by Andrews in 1984. We prove $$ c\phi_N(n)= \sum_{d \mid N} N/d \cdot P\left( \frac{ N}{d^2}n - \frac{N^2-
Externí odkaz:
http://arxiv.org/abs/2104.10250
Autor:
Aygin, Zafer Selcuk
Let $k \geq 2$ and $N$ be positive integers and let $\chi$ be a Dirichlet character modulo $N$. Let $f(z)$ be a modular form in $M_k(\Gamma_0(N),\chi)$. Then we have a unique decomposition $f(z)=E_f(z)+S_f(z)$, where $E_f(z) \in E_k(\Gamma_0(N),\chi)
Externí odkaz:
http://arxiv.org/abs/2102.04278
Autor:
Aygin, Zafer Selcuk, Nguyen, Khoa D.
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 $\mathbb{Q}(\sqrt[3]{k^2m})$ is monogenic is $\gg N^{1/3}$ and $\ll N/(\log N)^{1/3-\epsilon}$ for any $\epsilon>0$. Assumin
Externí odkaz:
http://arxiv.org/abs/2009.02442
Autor:
Aygin, Zafer Selcuk
Publikováno v:
J. Math. Anal. Appl. 465 (2018), 690-702
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_{\chi}^{k-j}-1}{p_{\chi}^{k}-1}F_p(k,j;\tau)+ \frac{p_{\chi}^{k}-p_{\chi}^{k-j}}{p_{\chi}^{k}-1}F_p(k,j;p\tau
Externí odkaz:
http://arxiv.org/abs/1808.01049
Autor:
Aygin, Zafer Selcuk
Let $k,N \in \mathbb{N}$ 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 $f(z) \in M_{2k}(\Gamma_0(N))$ in terms of sum of divisors function. In particular
Externí odkaz:
http://arxiv.org/abs/1705.06032
Autor:
Aygin, Zafer Selcuk
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 $l_1,l_2,l_3,l_6 \in \mathbb{N}_0$, with $l_1+l_2+l_3+l_6=6$. We also apply our results to write newforms in $S_{3} (\Gamma_0 (24), \chi )$ in terms of
Externí odkaz:
http://arxiv.org/abs/1705.01244
Autor:
Aygin, Zafer Selcuk
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 sums $ \sum_{a+p b=n}\sigma(a)\sigma(b)$, $ \sum_{p_1a+p_2 b=n}\sigma
Externí odkaz:
http://arxiv.org/abs/1612.09054