A. Sheth

most citedEuler Products at the Centre and Applications to Chebyshev's Bias

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math.NT2025

Chebyshev's bias for modular forms

Shin-ya Koyama, Arshay Sheth

We study Chebyshev's bias for the signs of Fourier coefficients of cuspidal newforms on $Γ_{0} (N)$ . Our main result shows that the bias towards either sign is completely determined b…

math.NT2025

The Asai--Flach Euler system in $p$ -adic families

David Loeffler, Arshay Sheth

We show that the Euler system for the Asai representation corresponding to a Hilbert modular eigenform over a real quadratic field, constructed by Lei, Loeffler and Zerbes (2018),…

math.NT2024★ 1 cited

Euler Products at the Centre and Applications to Chebyshev's Bias

Arshay Sheth

Let $π$ be an irreducible cuspidal automorphic representation of $GL_{n} (A_{Q})$ with associated $L$ -function $L (s, π)$ . We study the behaviour of the partial Eu…

Chebyshev's bias for modular forms

The Asai--Flach Euler system in p-adic families

Euler Products at the Centre and Applications to Chebyshev's Bias

The Asai--Flach Euler system in $p$ -adic families