186 papers
This paper demonstrates that any parahoric group scheme over a henselian discretely valued field becomes reductive after a finite Galois extension, allowing it to be recovered as the smoothening of Galois invariants of a reductive model, a result that extends prior work to the wildly ramified case and confirms the Grothendieck–Serre conjecture for generically trivial parahoric torsors in sufficiently good residue characteristics.
This paper proves that every sufficiently large odd integer can be expressed as the sum of one square and fourteen fifth powers of primes, while every sufficiently large even integer can be written as the sum of one square, one biquadrate, and twelve fifth powers of primes.
This paper presents the fourth known primitive solution to the Diophantine equation , detailing the methodology used to discover it.
This paper formulates a -adic optimization problem for matrix factorization and investigates a heuristic method analogous to Principal Component Analysis (PCA) to solve it.
This paper introduces an overpartition analogue of Andrews and Dastidar's partition function , deriving its generating function and establishing congruences modulo 3, 5, and powers of 2 using classical -series identities.
This paper establishes a systematic connection between the -dimensional Prouhet--Tarry--Escott problem and combinatorial design theory, introducing new solution definitions, proving fundamental bounds, and developing construction methods using block designs and orthogonal arrays that generalize and unify numerous previous results.
This paper proves that the Möbius Disjointness Conjecture holds for a specific class of irregular, distal flows on the infinite-dimensional torus defined by a skew-product transformation with -smooth coefficients.
This short note proves a conjecture by Alekseyev, Amdeberhan, Shallit, and Vukusic regarding the 3-adic valuation of a cubic binomial sum.
This paper proves that the natural density of the sequence of Ulam numbers is zero, meaning the proportion of Ulam numbers within the interval approaches zero as tends to infinity.
This paper constructs group-theoretic analogues of Johnson/Morita cocycles for pro-l groups to define Galois-cohomological classes for smooth curves, which are then used to demonstrate the existence of a non-hyperelliptic curve whose Ceresa class has a torsion image under the l-adic Abel-Jacobi map.
This paper investigates the local cyclicity and the growth of rational point groups for isogeny classes of abelian varieties over finite fields characterized by Weil polynomials of the form , utilizing a specific criterion involving the coprimality of the polynomial's derivative and radical at .
This paper improves the current upper and lower bounds for the Heilbronn triangle problem by applying concepts from the geometry of compression, establishing that the minimal triangle area for points on a unit disk satisfies and .
Using the compression method, this paper generalizes lower bounds for the Erdős unit distance and distinct distance problems to higher dimensions ( for ), providing alternative proofs and establishing new estimates for the number of distinct distances.
This paper proves and generalizes Z.-W. Sun's conjectures on infinite series involving harmonic numbers and binomial coefficients by evaluating them in closed form through their interpretation as automorphic objects on the moduli spaces of Legendre curves with genera 1, 2, 3, and 5.
This paper employs the particle motion bijection to establish new -series identities of the Andrews--Gordon type with parity restrictions on part multiplicities, thereby generalizing previous results and providing a simplified proof of a recent identity related to Ariki--Koike algebras.
This paper derives explicit formulas for the Iwasawa invariants of cyclotomic -extensions of multi-quadratic number fields using Hasse units and ramification analysis, and subsequently applies these results to establish criteria for determining the parity of their class numbers under Greenberg's conjecture.
Inspired by the work of Enriquez and Furusho, this paper provides a stabilizer interpretation for both the linearized double shuffle Lie algebra and its extension accommodating multiple q-zeta values and multiple Eisenstein series, demonstrating that these stabilizers preserve the extension between the two algebras.
This paper constructs higher Chow cycles of type on a family of degree abelian covers of branched over points and proves that for a very general member, these cycles generate a subgroup of the indecomposable part of rank at least by computing their images under the transcendental regulator map.
This paper establishes the conditions for the existence of the asymptotic mean value of ternary digits and identifies an infinite, everywhere dense set of numbers that possess this mean despite lacking a well-defined frequency for their digits.
This paper investigates transformations on the interval and functions that preserve the asymptotic mean of digits in the ternary (or -adic) representation of numbers, establishing the necessary and sufficient conditions for such transformations to belong to this class.