Results 31 to 40 of about 370,794 (154)
On the moments of exponential sums over r$r$‐free polynomials
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
wiley +1 more source
Random Diophantine inequalities of additive type [PDF]
, 2012 Using the Davenport–Heilbronn circle method, we show that for almost all additive Diophantine inequalities of degree k in more than 2k variables the expected asymptotic formula for the density of solutions holds ...
Dietmann, Rainer, Brüdern, Jörg
core +1 more source
Multiplicatively dependent integer vectors on a hyperplane
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract We establish several asymptotic formulae and upper bounds for the count of multiplicatively dependent integer vectors that lie on a fixed affine hyperplane and have bounded height. This work constitutes a direct extension of the results obtained by Pappalardi, Sha, Shparlinski, and Stewart.
Muhammad Afifurrahman +2 more
wiley +1 more source
Diophantine transference inequalities : weighted, inhomogeneous, and intermediate exponents [PDF]
, 2020 We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneoustransference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine approximation on
Ghosh, Anish +6 more
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Old and new conjectured diophantine inequalities [PDF]
Bulletin of the American Mathematical Society, 1990 This paper is a general survey of certain Diophantine conjectures of current interest, and relations between them. In this case, the discussion revolves around the Szpiro conjecture relating the modular height and conductor of elliptic curves defined over a fixed number field. The author shows that this is equivalent to the ``\(abc\)'' conjecture (if \(
openaire +4 more sources
On the Frobenius number of a modular Diophantine inequality [PDF]
Mathematica Bohemica, 2008 Summary: We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality \(ax\bmod b\leq x\), with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.
Rosales, José Carlos, Vasco, Paulo
openaire +2 more sources
Random Diophantine equations in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley +1 more source
On some diophantine inequalities involving primes.
Journal Fur Die Reine Und Angewandte Mathematik, 1967 exaly +3 more sources
New results on embeddings of self‐similar sets via renormalization
Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.Abstract For self‐similar sets X,Y⊆R$X,Y\subseteq \mathbb {R}$, we obtain new results toward the affine embeddings conjecture of Feng–Huang–Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of X,Y$X,Y$ have algebraic contraction ratios, and also for arbitrary Y$Y$ when the maps ...
Amir Algom, Michael Hochman, Meng Wu
wiley +1 more source
Moderate Deviation Principles for Lacunary Trigonometric Sums
Mathematische Nachrichten, Volume 299, Issue 5, Page 1028-1044, May 2026.ABSTRACT Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm.
Joscha Prochno, Marta Strzelecka
wiley +1 more source