Anne-Maria Ernvall-Hytonen

activity

20172024

most citedOn a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of

ϑ_{4}

1 citations · 1 across the 4 of their papers we have counts for

collaborators

5 papers

math.NT2024

Explicit estimates for the Goldbach summatory function

Gautami Bhowmik, Anne-Maria Ernvall-Hytönen, Neea Palojärvi

In order to study the analytic properties of the Goldbach generating function we consider a smooth version, similar to the Chebyshev function for the Prime Number Theorem. In this…

math.NT2023

Explicit estimates for the sum $\sum_{k = 0}^{n} k! (k n)^{2} (- 1)^{k}$

Anne-Maria Ernvall-Hytönen, Tapani Matala-aho

We are interested in finding an explicit estimate to the binomial sum $Q_{n} (x) = \sum_{k = 0}^{n} k! (k n)^{2} (- x)^{k}$ at $x = 1$ for $n = 0, 1, 2, \dots$ . Despite of its own interest…

math.NT2023

Transcendence measure of $e^{1/ n}$

Marta Dujella, Anne-Maria Ernvall-Hytönen, Linda Frey +1

For a given transcendental number $ξ$ and for any polynomial $P (X) =: λ_{0} + \dots + λ_{k} X^{k} \in Z [X]$ , we know that $P (ξ) \neq = 0.$ Let $k \geq 1$ and $ω (k, H)$ be the infimum…

math.NT2019

On Fourth and Higher Moments of Short Exponential Sums Related to Cusp Forms

Anne-Maria Ernvall-Hytönen, Esa V. Vesalainen

We obtain upper bounds for the fourth and higher moments of short exponential sums involving Fourier coefficients of holomorphic cusp forms twisted by rational additive twists with…

math.NT2017★ 1 cited

On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of $ϑ_{4}$

Anne-Maria Ernvall-Hytönen, Esa V. Vesalainen

Faulhuber and Steinerberger conjectured that the logarithmic derivative of $ϑ_{4}$ has the property that $y^{2} ϑ_{4}^{'} (y) / ϑ_{4} (y)$ is strictly decreasing and stri…

Explicit estimates for the Goldbach summatory function

Explicit estimates for the sum ∑k=0n​k!(kn​)2(−1)k

Transcendence measure of e1/n

On Fourth and Higher Moments of Short Exponential Sums Related to Cusp Forms

On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of ϑ4​

Explicit estimates for the sum $\sum_{k = 0}^{n} k! (k n)^{2} (- 1)^{k}$

Transcendence measure of $e^{1/ n}$

On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of $ϑ_{4}$