of integers with restricted digits. here \(e(x)=e^{2\pi i x}\) is the complex exponential function. we need to make use of various numerical estimates throughout the paper, some of which succeed only by a small margin. we have endeavored to avoid too many explicit calculations and we...
This is obtained by decorrelating Diophantine conditions which dictate when the Fourier transform of the primes is large from digital conditions which dictate when the Fourier transform of numbers with restricted digits is large. These estimates rely on a combination of the geometry of numbers, the ...
#数学##质数#Primes with restricted digits 有限位数的质数 【原文链接O网页链接】 摘要: 设a0∈{0…9},我们证明有无限个质数在它们的十进制展开式中没有数字a0。该证明是Hardy-Littlewood圆法在二元问题上的一个应用,其依据是获得适当的“I型”和“II型”算术信息,以用于Harman筛管来控制小弧。这是通过将丢...
primesinprogressionmultiplicativefunctionsLet denote the number of primes with . Chebyshev's bias is the phenomenon for which ''more often'' \\\pi(x;d... Pieter,Moree - 《Math Comp》 被引量: 34发表: 2004年 ON A CONJECTURE OF CUSICK CONCERNING THE SUM OF DIGITS OF n AND n plus t Fo...
we have before us an algorithm with exponential running time O(2 log 2 n ) . To quote Gauss again from article 329 of his Disquisitiones: Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special ...
This is\nobtained by decorrelating Diophantine conditions which dictate when the Fourier\ntransform of the primes is large from digital conditions which dictate when the\nFourier transform of numbers with restricted digits is large. These estimates\nrely on a combination of the geometry of numbers,...
Primes and Polynomials With Restricted Digitsdoi:10.1093/IMRN/RNAB002James MaynardOxford University Press (OUP)
The proof merges methods of Maynard from his paper on the infinitude of primes with restricted digits, results of Balog and Friedlander on Piatetski-Shapiro primes and the Hardy-Littlewood circle method in two variables. This is the first result on the ternary Goldbach problem with primes of ...
M. Drmota, C. Mauduit, J. Rivat, Primes with an average sum of digits. Compositio 145 (2), 271–292 (2009) MathSciNet MATHMichael Drmota, Christian Mauduit, and Joel Rivat. Primes with an average sum of digits. Compos. Math., 145(2):271-292, 2009....
Rivat, Primes with an average sum of digits, Compos. Math. 145 (2009), no. 2, 271-292.Michael Drmota, Christian Mauduit, and Joel Rivat. Primes with an average sum of digits. Compos. Math., 145(2):271-292, 2009.M. Drmota, C. Mauduit, and J. Rivat, Primes with an average ...