Results 11 to 20 of about 769 (62)
On the Davenport-Heilbronn theorems and second order terms
Inventiones Mathematicae, 2012 We give simple proofs of the Davenport--Heilbronn theorems, which provide the main terms in the asymptotics for the number of cubic fields having bounded discriminant and for the number of 3-torsion elements in the class groups of quadratic fields having
Bhargava, Manjul +2 more
core +3 more sources
Waring’s problem with shifts [PDF]
, 2015 Let µ1, . . . , µs be real numbers, with µ1 irrational. We investigate sums of shifted kth powers F(x1, . . . , xs) = (x1−µ1)k+. . .+(xs−µs) k. For k > 4, we bound the number of variables needed to ensure that if η is real and τ > 0 is sufficiently
Chow, Sam
core +3 more sources
A Diophantine approximation problem with two primes and one k-power of a prime [PDF]
, 2018 We refine a result of the last two Authors on a Diophantine approximation problem with two primes and a k-th power of a prime which was only proved to hold for ...
Alessandro, Gambini +2 more
core +1 more source
Tabulation of cubic function fields via polynomial binary cubic forms
, 2010 We present a method for tabulating all cubic function fields over $\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\mathbb{F}_{q}^*$, up to a given bound $B$ on the ...
Jacobson Jr., Michael +2 more
core +5 more sources
Exceptional sets for Diophantine inequalities [PDF]
, 2012 We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument.
D. Wooley, Scott T. Parsell, Trevor
core +1 more source
Counting integral points on symmetric varieties with applications to arithmetic statistics
Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.Abstract In this article, we combine Bhargava's geometry‐of‐numbers methods with the dynamical point‐counting methods of Eskin–McMullen and Benoist–Oh to develop a new technique for counting integral points on symmetric varieties lying within fundamental domains for coregular representations.
Arul Shankar +2 more
wiley +1 more source
Sums of two squares and a power
, 2016 We extend results of Jagy and Kaplansky and the present authors and show that for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for $k\not\equiv 0 \bmod 4$ a
C. Hooley +10 more
core +1 more source
Who in the world are the Heruli?1
Early Medieval Europe, Volume 32, Issue 3, Page 284-305, August 2024.The history of the Heruli represents a historical conundrum. Because of the poor state of the sources, caution is required when analysing this subject. However, the peculiarity of the case encourages us to rethink the way we conceive of and describe migrations in Late Antiquity.
Salvatore Liccardo
wiley +1 more source
On some reasons for doubting the Riemann hypothesis [PDF]
, 2003 Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of $|\zeta(1/2+it)|$ on the critical line, and zeros of a class of ...
Ivić, Aleksandar
core
Alon's Nullstellensatz for multisets
, 2011 Alon's combinatorial Nullstellensatz (Theorem 1.1 from \cite{Alon1}) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $\F$ be a field, $S_1,S_2,..., S_n$ be finite nonempty subsets of $\F$.
Kós, Géza, Rónyai, Lajos
core +1 more source