Cover Image

Two dimensional arithmetic progressions avoiding squares

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Dietmann, Rainer, Elsholtz, Christian
Format:	Preprint
Published:	2026
Subjects:	Number Theory Primary: 11B25, Secondary: 11D09, 11P70
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Sieving with square conditions and applications to Hilbert cubes in arithmetic sets
by: Dietmann, Rainer, et al.
Published: (2026)

Hilbert cubes in sets with arithmetic properties
by: Croot, Ernie, et al.
Published: (2026)

Finite sequences of integers expressible as sums of two squares
by: Choudhry, Ajai, et al.
Published: (2023)

Diophantine approximation with one prime, two squares of primes and one $k$-th power of a prime
by: Gambini, Alessandro
Published: (2017)

The Kloosterman circle method and weighted representation numbers of quadratic forms
by: Jones, Edna
Published: (2024)

Cubic Polynomials and Sums of Two Squares
by: Iyer, Siddharth
Published: (2025)

Restricted sumsets in multiplicative subgroups
by: Yip, Chi Hoi
Published: (2023)

The maximum size of sumsets in finite cyclic groups
by: Goswami, Vivekanand, et al.
Published: (2025)

Restricted sums of sets of cardinality $2p + 1$ in $\mathbb{Z}_p^2$
by: Terkel, Jacinda
Published: (2024)

Sárközy's theorem in $\mathbf{F}_2[x]$
by: Kowalska, Aleksandra
Published: (2025)

Structure of sets with small product sets in torsion-free groups, cyclic groups of prime orders and abelian groups
by: Mistri, Raj Kumar, et al.
Published: (2026)

Direct and Inverse Problems for Restricted Signed Sumsets -- I
by: Mistri, Raj Kumar, et al.
Published: (2025)

Direct and Inverse Problems for Restricted Signed Sumsets -- II
by: Mistri, Raj Kumar, et al.
Published: (2025)

Quadratic Gauss sums over $\mathbb{Z}^n/c\mathbb{Z}^n$: explicit formulas, a duality theorem, and applications to Weil representations and cubic hypersurfaces over $\mathbb{F}_p$
by: Zhu, Xiao-Jie
Published: (2025)

Rational lines on cubic hypersurfaces II
by: Brandes, Julia, et al.
Published: (2023)

Restricted set addition in finite abelian groups
by: Goswami, Vivekanand, et al.
Published: (2026)

The extensibility of the Diophantine triple $\{2, b, c\}$
by: Adžaga, Nikola, et al.
Published: (2026)

A Balanced Three-term Generalization of Nicomachus' Identity
by: Kim, Seon-Hong, et al.
Published: (2025)

Characterization of order structures avoiding three-term arithmetic progressions
by: Hirose, Minoru, et al.
Published: (2024)

Constructing Thick $B_h$-sets
by: O'Bryant, Kevin
Published: (2023)

Diophantine equation related to angle bisectors and solutions of Pell's equations
by: Hirotsu, Takashi
Published: (2022)

End behavior of Ramanujan's taxicab numbers
by: Benfield, Brennan, et al.
Published: (2024)

An alternating sum of the floor function of square roots
by: Chamberland, Marc, et al.
Published: (2025)

Generalized Perfect Matrices
by: Oertel, Alexander, et al.
Published: (2026)

An inverse theorem on sets with rich additive structure modulo primes
by: Croot, Ernie, et al.
Published: (2025)

Partitions into Triples with Equal Products and Families of Elliptic Curves
by: Youmbai, Ahmed El Amine, et al.
Published: (2024)

The trigonometric polynomial on sums of two squares, an additive problem and generalisation
by: Ramare, Olivier, et al.
Published: (2025)

Analytic expressions pertaining to certain arithmetical functions
by: Maw, Aung Phone
Published: (2024)

On extreme values of $r_3(n)$ in arithmetic progressions
by: Filaseta, Michael, et al.
Published: (2024)

Asymptotics For Local Solubility Of Diagonal Quadrics Over A Split Quadric Surface
by: Wilson, Cameron
Published: (2024)

Critical probabilistic characteristics of the Cramér model for primes and arithmetical properties
by: Weber, Michel
Published: (2021)

The arithmetic of critical values I: equicritical quartic polynomials
by: Naccarato, Francesco
Published: (2024)

An asymptotic formula with power-saving error term for counting prime solutions to a binary additive problem
by: Guria, Rachita
Published: (2024)

Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields
by: Elsholtz, Christian, et al.
Published: (2024)

Quartic reductions and elliptic obstructions for perfect Euler bricks
by: Peschmann, René
Published: (2026)

Elementary Proof of the Completeness of OEIS A051221 Below 2000
by: Azuma, Seiichi
Published: (2025)

On restricted sumsets with bounded degree relations
by: Ouyang, Minghui
Published: (2025)

An elementary proof of the theorem on the imaginary quadratic fields with class number 1
by: Carter, James E.
Published: (2024)

Courbes et fibrés vectoriels en théorie de Hodge $z$-adique globale
by: Li-Huerta, Siyan Daniel
Published: (2026)

Benford's Law in the ring $\mathbb{Z}(\sqrt{D})$
by: Patterson, Christine, et al.
Published: (2024)