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Explicit construction of self-dual integral normal bases for the square-root of the inverse different

Related publications (23)

Non-planarity of Markoff graphs mod p

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

European Mathematical Soc-Ems2024

The multivariate Serre conjecture ring

Luc Guyot

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

Academic Press Inc Elsevier Science2023

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

Thomas Mountford, Michael Cranston

In this paper we use the Riemann zeta distribution to give a new proof of the Erdos-Kac Central Limit Theorem. That is, if zeta(s) = Sigma(n >= 1) (1)(s)(n) , s > 1, then we consider the random variable X-s with P(X-s = n) = (1) (zeta) ( ...

Amer Mathematical Soc2023

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Eva Bayer Fluckiger, Ting-Yu Lee

Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...

Hebrew Univ Magnes Press2023

Automated mixing of maximally localized Wannier functions into target manifolds

Nicola Marzari, Giovanni Pizzi, Junfeng Qiao

Maximally localized Wannier functions (MLWFs) are widely used in electronic-structure calculations. We have recently developed automated approaches to generate MLWFs that represent natural tight-binding sets of atomic-like orbitals; these describe accurate ...

Nature Portfolio2023

Multiplicative chaos of the Brownian loop soup

Antoine Pierre François Jego, Titus Lupu

We construct a measure on the thick points of a Brownian loop soup in a bounded domain D

D

of the plane with given intensity theta>0

\theta >0

, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...

WILEY2023

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

Fourier uniqueness and interpolation in Euclidean space

Martin Peter Stoller

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

EPFL2022

Computation Of A 30750-Bit Binary Field Discrete Logarithm

Arjen Lenstra, Robert Granger, Thorsten Kleinjung, Benjamin Pierre Charles Wesolowski

This paper reports on the computation of a discrete logarithm in the finite field F-230750, breaking by a large margin the previous record, which was set in January 2014 by a computation in F-29234. The present computation made essential use of the elimina ...

AMER MATHEMATICAL SOC2021

Three-dimensional fluid-driven stable frictional ruptures

Brice Tanguy Alphonse Lecampion, Alexis Alejandro Sáez Uribe

We investigate the quasi-static growth of a fluid-driven frictional shear crack that propagates in mixed mode (II+III) on a planar fault interface that separates two identical half-spaces of a three-dimensional solid. The fault interface is characterized b ...

2022

D

of the plane with given intensity theta>0

\theta >0

, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...

WILEY2023