Steven Creech

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math.NT2025

Second Moment of Central Values of Half-Integral Weight Modular Forms and Subconvexity

Steven Creech, Henry Twiss, Zhining Wei +1

We let $f$ be a half-integral weight modular form of weight $κ > 4$ on $Γ_{0} (4)$ that is an eigenfunction of all Hecke operators $T_{n}$ , so that $T_{n} f = Λ_{f} (n) n^{\frac{κ - 1}{2}} f$ . Let…

math.NT2025

Explicit zero-free regions for automorphic $L$ -functions

Steven Creech, Alia Hamieh, Simran Khunger +3

Let $L (s, f)$ be the $L$ -function associated with a newform $f$ of even weight $k$ , squarefree level $N$ and trivial nebentypus. In this paper, we establish a new explicit zero-free…

math.NT2025

Cancellation in Sums of Hecke Eigenvalues Over Quadratic Polynomials and Mass Equidistribution

Steven Creech

We study cancellation in sums of Hecke eigenvalues over irreducible quadratic polynomials over short intervals. In particular, we look at an average over bases of Hecke forms of we…

math.NT2023

A Formula For the Number of $k$ -almost Primes

Steven Creech

In 2005, E. Noel and G. Panos constructed a formula to count the number of semiprimes less than a given value $x$ . In 2006, this formula was rediscovered independently by R.G. Wils…

Second Moment of Central Values of Half-Integral Weight Modular Forms and Subconvexity

Explicit zero-free regions for automorphic L-functions

Cancellation in Sums of Hecke Eigenvalues Over Quadratic Polynomials and Mass Equidistribution

A Formula For the Number of k-almost Primes

Explicit zero-free regions for automorphic $L$ -functions

A Formula For the Number of $k$ -almost Primes