Results 11 to 20 of about 366 (35)

A uniform estimate for the density of rational points on quadrics [PDF]

, 2018
This paper is concerned with the density of rational points of bounded height lying on a variety defined by an integral quadratic form Q. In the case of four variables, we give an estimate that does not depend on the coefficients of Q. For more variables,
Comtat, Félicien
core   +3 more sources

Fractional parts of Dedekind sums [PDF]

, 2015
Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec~(1997) on double exponential sums with Kloosterman fractions, we establish a uniformity of distribution result for the fractional parts of Dedekind sums $s(m,n)$
Banks, William D., Shparlinski, Igor E.
core   +1 more source

Cubic Thue inequalities with positive discriminant [PDF]

, 2013
We will give an explicit upper bound for the number of solutions to cubic inequality |F(x, y)| \leq h, where F(x, y) is a cubic binary form with integer coefficients and positive discriminant D.
Akhtari, Shabnam
core   +1 more source

Equal sums of like polynomials [PDF]

, 2005
Let $f$ be a polynomial of degree $d>6$, with integer coefficients. Then the paucity of non-trivial positive integer solutions to the equation $f(a)+f(b)=f(c)+f(d)$ is established.
Browning, T. D.
core   +1 more source

Characterizing algebraic curves with infinitely many integral points

, 2009
A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C over a number field is finite unless C has genus 0 and at most two points at infinity. In this paper we give necessary and sufficient conditions for C to have
Bilu, Yuri, Dimitrios, Poulakis, Paraskevas, Alvanos   +2 more
core   +2 more sources

On large $F$-Diophantine sets

, 2017
Let $F\in\mathbb{Z}[x,y]$ and $m\ge2$ be an integer. A set $A\subset \mathbb{Z}$ is called an $(F,m)$-Diophantine set if $F(a,b)$ is a perfect $m$-power for any $a,b\in A$ where $a\ne b$.
El-Sissi, Nermine, Sadek, Mohammad
core   +1 more source

Average Analytic Ranks of Elliptic Curves over Number Fields

Forum of Mathematics, Sigma
We give a conditional bound for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the ...
Tristan Phillips
doaj   +1 more source

The Manin–Peyre conjecture for smooth spherical Fano varieties of semisimple rank one

Forum of Mathematics, Sigma
The Manin–Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as well as some higher-dimensional smooth spherical Fano varieties.
Valentin Blomer, Jörg Brüdern, Ulrich Derenthal, Giuliano Gagliardi   +3 more
doaj   +1 more source

A Mean Value Theorem for the Diophantine Equation $axy-x-y=n$

, 2011
In this paper, we prove an asymptotic formula for the average number of solutions to the Diophantine equation $axy-x-y=n$ in which $a$ is fixed and and $n$ varies.Comment: 11 pages, to appear in Acta Math. Hungar. A couple of typos are corrected in the
Huang, Jing-Jing
core   +1 more source

Theta functions, fourth moments of eigenforms and the sup-norm problem II

Forum of Mathematics, Pi
Let f be an $L^2$ -normalized holomorphic newform of weight k on $\Gamma _0(N) \backslash \mathbb {H}$ with N squarefree or, more generally, on any hyperbolic surface $\Gamma \backslash \mathbb {H}$ attached to an Eichler order of ...
Ilya Khayutin, Paul D. Nelson, Raphael S. Steiner   +2 more
doaj   +1 more source