Akash Jim

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math.NT2024

On the average size of the eigenvalues of the Hecke operators

William Cason, Akash Jim, Charlie Medlock +2

We determine the average size of the eigenvalues of the Hecke operators acting on the cuspidal modular forms space $S_{k} (Γ_{0} (N))$ in both the vertical and the horizontal perspective…

math.NT2024

Nonvanishing of Second Coefficients of Hecke Polynomials on the Newspace

William Cason, Akash Jim, Charlie Medlock +3

For $m \geq 1$ , let $N \geq 1$ be coprime to $m$ , $k \geq 2$ , and $χ$ be a Dirichlet character modulo $N$ with $χ (- 1) = (- 1)^{k}$ . Then let $T_{m}^{new} (N, k, χ)$ denote the restric…

math.NT2024

The Galois Group of $x^{2 p} + b x^{p} + c^{p}$ over $Q$

Akash Jim, Thomas Hagedorn

We prove an irreducibility criterion for polynomials of the form $h (x) = x^{2 m} + b x^{m} + c_{1} \in F [x]$ relating to the Dickson polynomials of the first kind $D_{p}$ . In the case when $…

On the average size of the eigenvalues of the Hecke operators

Nonvanishing of Second Coefficients of Hecke Polynomials on the Newspace

The Galois Group of x2p+bxp+cp over Q

The Galois Group of $x^{2 p} + b x^{p} + c^{p}$ over $Q$