A. Sheth

activity

20232026

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

1 citations · 1 across the 8 of their papers we have counts for

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math.NT2026

Products of point counts of higher genus curves over finite fields

Alina Bucur, Kiran S. Kedlaya, Arshay Sheth

Let $E / Q$ be an elliptic curve and for each prime $p$ , let $N_{p}$ denote the number of points of $E$ modulo $p$ . The original version of the conjecture of Birch and Swinnert…

math.NT2026

Real geometric transcendence for the Gamma function

Arshay Sheth

We show that the $x$ -axis is the only real algebraic curve in $R^{2}$ whose image via the Gamma function is contained in an algebraic curve. Our proof employs an elegant base…

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

Real geometric transcendence for uniformization maps of algebraic Riemann surfaces

Arshay Sheth, Matteo Tamiozzo

Let $X$ be a smooth connected complex algebraic curve that is not simply connected, and let $X ~$ be the universal cover of $X$ . We study the set of irreducible real algebrai…

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

On the $p$ -ranks of class groups of certain Galois extensions

Ufuoma Asarhasa, Rusiru Gambheera, Debanjana Kundu +2

Let $p$ be an odd prime, let $N$ be a prime with $N \equiv 1 (mod p)$ , and let $ζ_{p}$ be a primitive $p$ -th root of unity. We study the $p$ -rank of the class group of $\mathbb{Q}(ζ…

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…

math.NT2024

Control Theorems for Hilbert Modular Varieties

Arshay Sheth

We prove an exact control theorem, in the sense of Hida theory, for the ordinary part of the middle degree étale cohomology of certain Hilbert modular varieties, after localizing a…

math.NT2023

Euler Product Asymptotics for $L$ -functions of Elliptic Curves

Arshay Sheth

Let $E / Q$ be an elliptic curve and for each prime $p$ , let $N_{p}$ denote the number of points of $E$ modulo $p$ . The original version of the Birch and Swinnerton-Dyer conjec…

Products of point counts of higher genus curves over finite fields

Real geometric transcendence for the Gamma function

Chebyshev's bias for modular forms

Real geometric transcendence for uniformization maps of algebraic Riemann surfaces

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

On the p-ranks of class groups of certain Galois extensions

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

Control Theorems for Hilbert Modular Varieties

Euler Product Asymptotics for L-functions of Elliptic Curves

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

On the $p$ -ranks of class groups of certain Galois extensions

Euler Product Asymptotics for $L$ -functions of Elliptic Curves