## 222 Citations

On the Epstein zeta function and the zeros of a class of Dirichlet series

- Mathematics
- 2021

By generalizing the classical Selberg-Chowla formula, we establish the analytic continuation and functional equation for a large class of Epstein zeta functions. This continuation is studied in order…

Explicit asymptotics for certain single and double exponential sums

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2020

Abstract By combining classical techniques together with two novel asymptotic identities derived in recent work by Lenells and one of the authors, we analyse certain single sums of Riemann-zeta type.…

A Novel Integral Equation for the Riemann Zeta Function and Large t-Asymptotics

- MathematicsMathematics
- 2019

Based on the new approach to Lindelöf hypothesis recently introduced by one of the authors, we first derive a novel integral equation for the square of the absolute value of the Riemann zeta…

ABC implies no “Siegel zeros” for L-functions of characters with negative discriminant

- Mathematics
- 2000

Explicit Values for Ramanujan's Theta Function ϕ(q)

- MathematicsHardy-Ramanujan Journal
- 2022

This paper provides a survey of particular values of Ramanujan's theta function $\varphi(q)=\sum_{n=-\infty}^{\infty}q^{n^2}$, when $q=e^{-\pi\sqrt{n}}$, where $n$ is a positive rational number.…

Non-vanishing of symmetric cube $L$-functions

- Mathematics
- 2021

Abstract. We prove that there are infinitely many Maass–Hecke cuspforms over the field Q[ √ −3] such that the corresponding symmetric cube L-series does not vanish at the center of the critical…

On the real and complex zeros of the quadrilateral zeta function

- Mathematics
- 2020

Let $0 < a \le 1/2$ and define the quadrilateral zeta function by $2Q(s,a) := \zeta (s,a) + \zeta (s,1-a) + {\rm{Li}}_s (e^{2\pi ia}) + {\rm{Li}}_s(e^{2\pi i(1-a)})$, where $\zeta (s,a)$ is the…

On the location of the zero-free half-plane of a random Epstein zeta function

- Mathematics
- 2018

In this note we study, for a random lattice L of large dimension n, the supremum of the real parts of the zeros of the Epstein zeta function $$E_n(L,s)$$En(L,s) and prove that this random variable…

Evaluation and regularization of generalized Eisenstein series and application to 2D cylindrical harmonic sums

- Mathematics
- 2016

In the study of periodic media, conditionally convergent series are frequently encountered and their regularization is crucial for applications. We derive an identity that regularizes two-dimensional…

Lattices energies and variational calculus

- Mathematics
- 2015

In this thesis, we study minimization problems for discrete energies and we search to understand why a periodic structure can be a minimizer for an interaction energy, that is called a…