Anne-Maria Ernvall-Hytonen

activity

20102024

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

ϑ_{4}

1 citations · 1 across the 7 of their papers we have counts for

collaborators

9 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…

math.NT2014

On an approximate functional equation involving the divisor function

Anne-Maria Ernvall-Hytönen

The error term in the approximate functional equation for exponential sums involving the divisor function will be improved under certain conditions for the parameters of the approx…

math.NT2013

Mean square estimate for relatively short exponential sums involving Fourier coefficients of cusp forms

Anne-Maria Ernvall-Hytönen

We estimate the mean square of a short exponential sum involving Fourier coefficients of a cusp form with a linear twist, a smooth weight function, and a relatively short averaging…

math.NT2010

On the mean square of short exponential sums related to cusp forms

Anne-Maria Ernvall-Hytönen

The purpose of the article is to estimate the mean square of a squareroot length exponential sum of Fourier coefficients of a holomorphic cusp form.

math.NT2010

An improvement on the upper bound of exponential sums connected to holomorphic cusp forms

Anne-Maria Ernvall-Hytönen

We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.

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​

On an approximate functional equation involving the divisor function

Mean square estimate for relatively short exponential sums involving Fourier coefficients of cusp forms

On the mean square of short exponential sums related to cusp forms

An improvement on the upper bound of exponential sums connected to holomorphic cusp forms

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 $ϑ_{4}$