Arvind Kumar

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math.NT2026

Determining newforms via arithmetic relations among Fourier coefficients

Arvind Kumar, Moni Kumari, Prabhat Kumar Mishra

We investigate the distribution of primes satisfying arithmetic inequalities involving the Fourier coefficients of two non-CM newforms at prime powers. More precisely, we establish…

math.NT2026

Effective Joint Sato-Tate Distribution and Sign Change of Symmetric Power Coefficients

Arvind Kumar, Moni Kumari, Prabhat Kumar Mishra

We prove an unconditional, effective joint Sato--Tate distribution for the Fourier coefficients of two twist-inequivalent, non-CM newforms $f$ and $f^{'}$ . Our result generalises a re…

math.NT2024

Certain squarefree levels of reducible modular mod $ℓ$ Galois representations

Arvind Kumar, Prabhat Kumar Mishra

Let $k \geq 2$ be an even integer, $ℓ \geq max {5, k - 1}$ be a prime, and $N$ be a squarefree positive integer. It is known that if the $mod ℓ$ Galois representation $…

Determining newforms via arithmetic relations among Fourier coefficients

Effective Joint Sato-Tate Distribution and Sign Change of Symmetric Power Coefficients

Certain squarefree levels of reducible modular modℓ Galois representations

Certain squarefree levels of reducible modular mod $ℓ$ Galois representations