Tootfinder

Large quadratic character sums
Zikang Dong, Yanbin Zhang
https://arxiv.org/abs/2509.07651 https://arxiv.org/pdf/2509.07651…

Large quadratic character sums
In this article, we investigate conditional large values of quadratic Dirichlet character sums. We prove some Omega results of quadratic character sums under the assumption of the generalized Riemnn hypothesis, which are as sharp as previous results for all characters modulo a large prime.

Quadrature rules with few nodes supported on algebraic curves
Cordian Riener, Ettore Teixeira Turatti
https://arxiv.org/abs/2509.06643 https://arxiv.org/pd…

Quadrature rules with few nodes supported on algebraic curves
We investigate quadrature rules for measures supported on real algebraic and rational curves, focusing on the {odd-degree} case \(2s-1\). Adopting an optimization viewpoint, we minimize suitable penalty functions over the space of quadrature rules of strength \(2s-1\), so that optimal solutions yield rules with the minimal number of nodes. For plane algebraic curves of degree \(d\), we derive explicit node bounds depending on \(d\) and the number of places at infinity, improving results of Rien…

Reinforcement learning for online hyperparameter tuning in convex quadratic programming
Jeremy Bertoncini, Alberto De Marchi, Matthias Gerdts, Simon Gottschalk
https://arxiv.org/abs/2509.07404

Reinforcement learning for online hyperparameter tuning in convex quadratic programming
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow tail-convergence typical of first-order schemes, thus requiring many iterations to achieve high-accuracy solutions. Moreover, hyperparameter tuning significantly impacts on the solver performance but how to find an appropriate parameter configuration remains an elusive …

Infinite horizon quadratic backward stochastic differential equations driven by $G$-Brownian motion
Yiqing Lin, Yifan Sun, Falei Wang
https://arxiv.org/abs/2509.05706 https://…

Infinite horizon quadratic backward stochastic differential equations driven by $G$-Brownian motion
The aim is to prove the well-posedness of infinite horizon backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with quadratic generators. To this end, we provide a full construction of explicit solutions to linear $G$-BSDEs with unbounded coefficients and the linearization method under the quadratic assumption. In addition, the comparison theorems for both finite and infinite horizon $G$-BSDEs are established.

Neglected solutions in quadratic gravity
Breno L. Giacchini, Ivan Kol\'a\v{r}
https://arxiv.org/abs/2509.07317 https://arxiv.org/pdf/2509.07317

Neglected solutions in quadratic gravity
We report on several previously overlooked families of static spherically symmetric solutions in quadratic gravity. Our main result concerns the existence of solutions whose leading exponents depend on the ratio ${ω=α/(3β)}$ of the four-derivative couplings. We demonstrate that the space of models with ${ω>1}$ contains a dense set that admits non-Frobenius solutions ${(s_*, 2 - 3 s_*)_0}$ (in standard Schwarzschild coordinates), with certain rational numbers $s_*(ω)$. These solutions corre…

Super-Quadratic Quantum Speed-ups and Guessing Many Likely Keys
Timo Glaser, Alexander May, Julian Nowakowski
https://arxiv.org/abs/2509.06549 https://arxi…

Super-Quadratic Quantum Speed-ups and Guessing Many Likely Keys
We study the fundamental problem of guessing cryptographic keys, drawn from some non-uniform probability distribution $D$, as e.g. in LPN, LWE or for passwords. The optimal classical algorithm enumerates keys in decreasing order of likelihood. The optimal quantum algorithm, due to Montanaro (2011), is a sophisticated Grover search. We give the first tight analysis for Montanaro's algorithm, showing that its runtime is $2^{H_{2/3}(D)/2}$, where $H_α(\cdot)$ denotes Renyi entropy with paramete…

Limit Cycles in Piecewise Quadratic Kolmogorov Systems
Leonardo Da Cruz, Regilene Oliveira, Joan Torregrosa
https://arxiv.org/abs/2509.06198 https://arxiv.…

Limit Cycles in Piecewise Quadratic Kolmogorov Systems
We study planar piecewise quadratic differential systems of Kolmogorov type. Specifically, we consider systems with both coordinate axes invariant and with a separation line that is straight and distinct from the invariant axes. The main results concern two different aspects. First, the center problem is solved for certain subclasses. Second, using this classification, the bifurcation of limit cycles of crossing type is investigated. We contrast the nature of Hopf-type bifurcations in smooth an…

Strong instability of standing waves for a system of nonlinear Klein-Gordon equations with quadratic interaction
Masahito Ohta
https://arxiv.org/abs/2509.06583 https://

Strong instability of standing waves for a system of nonlinear Klein-Gordon equations with quadratic interaction
We consider a system of nonlinear Klein-Gordon equations with quadratic interaction in two and three space dimensions. The strong instability of standing wave solutions is studied for the system without assuming the mass resonance condition.

Generalized Sato-Tate and quadratic residues
Sergey Vladuts
https://arxiv.org/abs/2509.07183 https://arxiv.org/pdf/2509.07183

Generalized Sato-Tate and quadratic residues
We show that the Generalized Sato-Tate Conjecture permits to obtain rather precise information on the distribution of the consecutive quadratic residues modulo large primes.

Nagell-Lutz theorem for imaginary quadratic fields of class number one
Leena Mondal, Amrutha C
https://arxiv.org/abs/2509.07524 https://arxiv.org/pdf/2509.…

Nagell-Lutz theorem for imaginary quadratic fields of class number one
We prove the Nagell-Lutz theorem for the imaginary quadratic fields of class number one.