L. Washington

activity

20082022

most citedIwasawa Invariants of Some Non-Cyclotomic

Z_{p}

-extensions

3 citations · 8 across the 6 of their papers we have counts for

collaborators

11 papers

math.NT2022★ 1 cited

Sums of Powers of Primes II

Lawrence C. Washington

For a real number $k$ , define $π_{k} (x) = \sum_{p \leq x} p^{k}$ . When $k > 0$ , we prove that $π_{k} (x) - π (x^{k + 1}) = Ω_{\pm} (\frac{x ^{\frac{1}{2} + k}}{lo g x} lo g lo g lo g x)$ as…

math.NT2021

An Elliptic Curve Analogue of Pillai's Lower Bound on Primitive Roots

Steven Jin, Lawrence C. Washington

Let $E / Q$ be an elliptic curve. For a prime $p$ of good reduction, let $r (E, p)$ be the smallest non-negative integer that gives the $x$ -coordinate of a point of maximal or…

math.NT2021

Dirichlet Series Expansions of p-adic L-Functions

Heiko Knospe, Lawrence C. Washington

We study $p$ -adic $L$ -functions $L_{p} (s, χ)$ for Dirichlet characters $χ$ . We show that $L_{p} (s, χ)$ has a Dirichlet series expansion for each regularization parameter $c$ that is prim…

math.NT2020

Class group of real cyclotomic fields

Mohit Mishra

In this article, we prove that every finite abelian group $G$ of odd order occurs as a subgroup of the class group of infinitely many real cyclotomic fields.

math.NT2020★ 3 cited

Analogues of the Robin-Lagarias Criteria for the Riemann Hypothesis

Lawrence C. Washington, Ambrose Yang

Robin's criterion states that the Riemann hypothesis is equivalent to $σ (n) < e^{γ} n lo g lo g n$ for all integers $n \geq 5041$ , where $σ (n)$ is the sum of divisors of $n$ and $γ$ is…

math.NT2018

Explicit computations in Iwasawa theory

Reinier Broker, David Hubbard, Lawrence C. Washington

We give two algorithms to compute layers of the anticyclotomic $Z_{3}$ -extension of an imaginary quadratic field. The first is based on complex multiplication techniques for no…