Tianyu Ni

activity

20242026

collaborators

7 papers

math.NT2026

Rational spanning sets of level-one cusp forms from Eisenstein series at prime levels

Tianyu Ni

Let $S_{k}$ be the space of cusp forms of weight $k$ for the full modular group $SL_{2} (Z)$ . In this paper, we will exhibit an explicit rational spanning subset of $S_{k}$ …

math.NT2026

Explicit generators of the space of modular forms

Tianyu Ni, Ashley Song, Yanhui Su +2

Let $S_{I^} º$ be the space of cusp forms of weight $I^º$ and level one, and let $S_{I^} º^{*}$ denote its dual space. In this paper, we find explicit spanning subsets of $S_{I^} º$ consisti…

math.NT2026

Representation of Ramanujan's tau function by twisted divisor functions

Tianyu Ni

We present an infinite family of identities that represent Ramanujan's tau function in terms of convolution sums of twisted divisor functions. Our method involves explicitly constr…

math.NT2026

Twisted periods of modular forms

Tianyu Ni, Hui Xue

Let $S_{k}$ denote the space of cusp forms of weight $k$ and level one. For $0 \leq t \leq k - 2$ and primitive Dirichlet character $I ¨ $ mod $D$ , we introduce twisted periods $r_{t, I ¨ }$ …

math.NT2025

Non-repetition of second coefficients of Hecke polynomials

Archer Clayton, Helen Dai, Tianyu Ni +3

Let $T_{m} (N, 2 k)$ denote the $m$ -th Hecke operator on the space $S_{2 k} (I^_{0} (N))$ of cuspidal modular forms of weight $2 k$ and level $N$ . In this paper, we study the non-repetition o…

math.NT2024

AGM aquariums and elliptic curves over arbitrary finite fields

June Kayath, Connor Lane, Ben Neifeld +2

In this paper, we define a version of the arithmetic-geometric mean (AGM) function for arbitrary finite fields $F_{q}$ , and study the resulting AGM graph with points $(a,b)…