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Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli
Peng Gao, Liangyi Zhao
https://arxiv.org/abs/2404.05081 https://

Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli
Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli of imaginary quadratic number fields of class number one under the generalized Riemann hypothesis. As corollaries, we evaluate asymptotically the first moment of central values as well as the one-level density of the families of L-functions under consideratio…

Polyhedral Analysis of Quadratic Optimization Problems with Stieltjes Matrices and Indicators
Peijing Liu, Alper Atamt\"urk, Andr\'es G\'omez, Simge K\"u\c{c}\"ukyavuz
https://arxiv.org/abs/2404.04236

Polyhedral Analysis of Quadratic Optimization Problems with Stieltjes Matrices and Indicators
In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a Stieltjes matrix, which naturally appears in sparse graphical inference problems and others. We describe an explicit convex formulation for the problem by studying the Stieltjes polyhedron arising as part of an extended formulation and exploiting the supermodularity of a set function defined on its extreme points. Our…

Quadratic varieties of small codimension
Kiwamu Watanabe
https://arxiv.org/abs/2405.04002 https://arxiv.org/pdf/2405.04002

Quadratic varieties of small codimension
Let $X \subset \mathbb P^{n+c}$ be a nondegenerate smooth projective variety of dimension $n$ defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that X is a complete intersection provided that $n\geq 2c+1$. As the extremal case, they also classified $X$ with $n=2c$. In this paper, we classify $X$ with $n=2c-1$.

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The quadratic tracking problem for systems with persistent memory in $\zzr^d$
Luciano Pandolfi
https://arxiv.org/abs/2404.04117 https://

The quadratic tracking problem for systems with persistent memory in $\zzr^d$
The classical quadratic regulator problem has rarely been studied for systems with persistent memory until recent times. In this paper we study the quadratic tracking problem on a \emph{ finite time horizon} for a system described by a controlled linear Volterra integrodifferential equation in $\zzr^d$. We use the Fredholm equation approach and we derive the synthesis of the optimal control in terms of a Riccati differential equation, independent of the reference signal, and of two equations wh…

Counting solutions to quadratic polynomials
V. Vinay Kumaraswamy
https://arxiv.org/abs/2405.04328 https://arxiv.org/pdf/2405.04328

Counting solutions to quadratic polynomials
Using the circle method, we obtain asymptotic formulae for the number of integer solutions to certain quadratic polynomials that are uniform in the coefficients of the polynomial.

On semidefinite descriptions for convex hulls of quadratic programs
Alex L. Wang, Fatma Kilinc-Karzan
https://arxiv.org/abs/2403.04752 https://

On semidefinite descriptions for convex hulls of quadratic programs
Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard semidefinite program (SDP) relaxation. In this paper we study when the convex hull of the epigraph of a QCQP coincides with the projected epigraph of the SDP relaxation. We present a sufficient condition for convex hull exactness and show that this condition is further necessary under an…

Unramified Iwasawa module of $\mathbb{Z}_2$-extension of certain quadratic fields with a bounded quotient
H Laxmi, Anupam Saikia
https://arxiv.org/abs/2404.05190

Unramified Iwasawa module of $\mathbb{Z}_2$-extension of certain quadratic fields with a bounded quotient
We consider an infinite family of real quadratic fields $k$ where the discriminant has three distinct odd prime factors, and the prime 2 splits. We show that the unramified Iwasawa module $X(k_{\infty})$ associated with the $\mathbb{Z}_2$-extension of $k$ has a bounded quotient. Thus, we also verify Greenberg's conjecture on the vanishing of Iwasawa invariants for such fields and obtain a finer structure for $X(k_{\infty})$.

This https://arxiv.org/abs/2310.03543 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$\mathbb{Z}_2$-extension of real quadratic fields with $\mathbb{Z}/2\mathbb{Z}$ as $2$-class group at each layer
Let $K= \mathbb{Q}(\sqrt{d})$ be a real quadratic field with $d$ having three distinct prime factors. We show that the $2$-class group of each layer in the $\mathbb{Z}_2$-extension of $K$ is $\mathbb{Z}/2\mathbb{Z}$ under certain elementary assumptions on the prime factors of $d$. In particular, it validates Greenberg's conjecture on the vanishing of the Iwasawa $λ$-invariant for a new family of infinitely many real quadratic fields.

Finite-time Linear-Quadratic Optimal Control of Partial Differential-Algebraic Equations
Ala' Alalabi, Kirsten Morris
https://arxiv.org/abs/2404.03766 …

Finite-time Linear-Quadratic Optimal Control of Partial Differential-Algebraic Equations
Finite-time linear-quadratic control of partial differential-algebraic equations (PDAEs) is considered. The discussion is restricted to those that are radial with index $0$; this corresponds to a nilpotency degree of 1. We establish the existence of a unique minimizing optimal control. A projection is used to derive a system of differential Riccati-like equation coupled with an algebraic equation, yielding the solution of the optimization problem in a feedback form. This generalizes the well-kn…