Results 1 to 10 of about 268 (51)
Diophantine approximation with one prime, two squares of primes and one kth power of a prime
Open Mathematics, 2021 Let ...
Gambini Alessandro
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On the Waring-Goldbach problem for two squares and four cubes
Open Mathematics, 2023 Let NN be a sufficiently large integer. In this article, it is proved that, with at most O(N112+ε)O\left({N}^{\tfrac{1}{12}+\varepsilon }) exceptions, all even positive integers up to NN can be represented in the form p12+p22+p33+p43+p53+p63{p}_{1}^{2 ...
Zhang Min, Bai Hongxin, Li Jinjiang
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The Mordell integral, quantum modular forms, and mock Jacobi forms
Research in Number Theory, 2015 It is explained how the Mordell integral ∫Reπiτx2−2πzxcosh(πx)dx $$\int_{\mathbb R} \frac{e^{\pi i \tau x^{2} - 2\pi zx}}{\cosh(\pi x)} dx $$ unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular ...
Bobbie Chern, Robert C. Rhoades
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A NOTE ON A THEOREM OF HEATH-BROWN AND SKOROBOGATOV [PDF]
, 2011 We generalise a result of Heath-Brown and Skorobogatov [7] to show that a certain class of varieties over a number field k satisfies Weak Approximation and the Hasse Principle, provided there is no Brauer–Manin obstruction.
M. Jones
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Short intervals asymptotic formulae for binary problems with primes and powers, I: density 3/2 [PDF]
, 2016 We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square.
A., Zaccagnini, Languasco, Alessandro
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On pairs of equations involving unlike powers of primes and powers of 2
, 2020 In this paper, it is proved that every pair of sufficiently large even integers can be represented by a pair of equations, each containing one prime, one prime square, two prime cubes and 302 powers of 2. This result constitutes a refinement upon that of
Yuhui Liu
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A pair of equations in unlike powers of primes and powers of 2
Open Mathematics, 2020 In this article, we show that every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of one prime, one prime squares, two prime cubes, and 187 powers of 2.
Cai Yong, Hu Liqun
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The integral part of a nonlinear form with a square, a cube and a biquadrate
Open Mathematics, 2020 In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{
Ge Wenxu, Li Weiping, Zhao Feng
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Mean value estimates for odd cubic Weyl sums [PDF]
, 2014 We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $\alpha x^3+\beta x$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's ...
Wooley, Trevor D.
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On sums of three squares [PDF]
, 2005 Let $r_3(n)$ be the number of representations of a positive integer $n$ as a sum of three squares of integers. We give two distinct proofs of a conjecture of Wagon concerning the asymptotic value of the mean square of $r_3(n)$.Comment: 11 pages, minor ...
Choi, S. K. K. +2 more
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