Olli Jarviniemi

activity

20192022

most citedOn large differences between consecutive primes

1 citations · 1 across the 3 of their papers we have counts for

collaborators

5 papers

math.NT2022★ 1 cited

On large differences between consecutive primes

Olli Järviniemi

We show that $p_{n} \in [x, 2 x] p_{n + 1} - p_{n} \geq x^{1/2} \sum (p_{n + 1} - p_{n}) ≪ x^{0.57 + ε}$ and $$\sum_{\substack{p_n \in [x, 2x] \\ p_{n+1} - p_n \ge x^{0.45}}}…

math.NT2021

Orders of algebraic numbers in finite fields

Olli Järviniemi

For an algebraic number $α$ we consider the orders of the reductions of $α$ in finite fields. In the case where $α$ is an integer, it is known by the work on Artin's primitive root…

math.NT2020

On the Common Prime Divisors of Polynomials

Olli Järviniemi

The prime divisors of a polynomial $P$ with integer coefficients are those primes $p$ for which $P (x) \equiv 0 (mod p)$ is solvable. Our main result is that the common prime divis…

math.NT2019

Equality of orders of a set of integers modulo a prime

Olli Järviniemi

For finitely generated subgroups $W_{1}, \dots, W_{t}$ of $Q^{\times}$ , integers $k_{1}, \dots, k_{t}$ , a Galois extension $F$ of $Q$ and a union of conjugacy classes…

math.NT2019

Simultaneous insolvability of exponential congruences

Olli Järviniemi

We determine a necessary and sufficient condition for the infinitude of primes $p$ such that none of the equations $a_{i}^{x} \equiv b_{i} (mod p), 1 \leq i \leq n,$ are solvable. We cont…