Results 11 to 20 of about 106 (53)
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
Birch's theorem with shifts [PDF]
, 2017 A famous result due to Birch (1961) provides an asymptotic formula for the number of integer points in an expanding box at which given rational forms of the same degree simultaneously vanish, subject to a geometric condition.
Chow, Samuel Khai Ho
core +6 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
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Lower bounds for numbers of ABC-hits [PDF]
, 1935 By an ABC-hit, we mean a triple (a,b,c) of relatively prime positive integers such that a+b=c and rad(abc)0 and X large enough N(X)⩾exp((logX)1/2−ϵ)
Dahmen, Sander R.
core +1 more source
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
Diophantine approximation by special primes
, 2018 We show that whenever $\delta>0$, $\eta$ is real and constants $\lambda_i$ satisfy some necessary conditions, there are infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality $|\lambda_1p_1 + \lambda_2p_2 + \lambda_3p_3+\eta|
Dimitrov, S. I.
core +1 more source
On a Diophantine problem with two primes and s powers of two
, 2009 We refine a recent result of Parsell on the values of the form $\lambda_1p_1 + \lambda_2p_2 + \mu_1 2^{m_1} + ...m + \mu_s 2^{m_s}, $ where $p_1,p_2$ are prime numbers, $m_1,...c, m_s$ are positive integers, $\lambda_1 / \lambda_2$ is negative and ...
Languasco, A., Zaccagnini, A.
core +3 more sources
The sup-norm problem for PGL(4)
, 2014 Let F be a Hecke-Maass cusp form for the group SL(4, Z) with Laplace eigenvalue lambda. Assume that F satisfies the Ramanujan conjecture at infinity (this is satisfied by almost all cusp forms).
Blomer, Valentin, Maga, Péter
core +1 more source
Volume and lattice points of reflexive simplices
, 2007 We prove sharp upper bounds on the volume and the number of lattice points on edges of higher-dimensional reflexive simplices. These convex-geometric results are derived from new number-theoretic bounds on the denominators of unit fractions summing up to
Nill, Benjamin
core +1 more source