A. Sheth

collaborators

5 papers

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.NT2026

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 $I^_{0} (N)$ . Our main result shows that the bias towards either sign is completely determined…

math.NT2026

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…

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),…

Real geometric transcendence for the Gamma function

Chebyshev's bias for modular forms

Euler Product Asymptotics for L-functions of Elliptic Curves

Real geometric transcendence for uniformization maps of algebraic Riemann surfaces

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

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

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