Results 11 to 20 of about 93,941 (183)
Uniform distribution modulo one: a geometrical viewpoint.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1981 MENDES FRANCE, M., DEKKING, F.M.
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Hardware acceleration of number theoretic transform for zk‐SNARK
Engineering Reports, EarlyView., 2023 An FPGA‐based hardware accelerator with a multi‐level pipeline is designed to support the large‐bitwidth and large‐scale NTT tasks in zk‐SNARK. It can be flexibly scaled to different scales of FPGAs and has been equipped in the heterogeneous acceleration system with the help of HLS and OpenCL.
Haixu Zhao +6 more
wiley +1 more source
, 2020 We investigate the distribution of $\alpha p$ modulo one in imaginary quadratic number fields $\mathbb{K}\subset\mathbb{C}$ with class number one, where $p$ is restricted to prime elements in the ring of integers $\mathcal{O} = \mathbb{Z}[\omega]$ of ...
Baier, Stephan, Technau, Marc
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Genericity and UD-random reals [PDF]
, 2015 Avigad introduced the notion of UD–randomness based in Weyl’s 1916 definition of uniform distribution modulo one. We prove that there exists a weakly 1–random real that is neither UD–random nor weakly 1–generic.
Calvert, Wesley, Franklin, Johanna
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Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory [PDF]
, 2020 The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory.
Chacón, Iván Blanco
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Uniform distribution modulo one on subsequences [PDF]
Proceedings of the American Mathematical Society, 1999 Let P \mathcal {P} be a set of primes with a divergent series of reciprocals and let K = K ( P ) \mathcal {K} = \mathcal {K}(\mathcal {P} ) denote the set of squarefree integers greater than one that are divisible ...
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Finite-state Markov Chains obey Benford's Law [PDF]
, 2010 A sequence of real numbers (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) are distributed logarithmically.
Berger, Arno +3 more
core +8 more sources
ON THE DISTRIBUTION OF TORSION POINTS MODULO PRIMES [PDF]
Bulletin of the Australian Mathematical Society, 2012 AbstractLet $\Bbb A$ be a commutative algebraic group defined over a number field K. For a prime ℘ in K where $\Bbb A$ has good reduction, let N℘,n be the number of n-torsion points of the reduction of $\Bbb A$ modulo ℘ where n is a positive integer. When $\Bbb A$ is of dimension one and n is relatively prime to a fixed finite set of primes depending ...
Chen, Yen-Mei J., Kuan, Yen-Liang
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Log-correlated Gaussian fields: an overview [PDF]
, 2014 We survey the properties of the log-correlated Gaussian field (LGF), which is a centered Gaussian random distribution (generalized function) $h$ on $\mathbb R^d$, defined up to a global additive constant. Its law is determined by the covariance formula $$
Duplantier, Bertrand +3 more
core +4 more sources
Trigonometric approximation and uniform distribution modulo one [PDF]
Proceedings of the American Mathematical Society, 1988 We construct n n -dimensional versions of the Beurling and Selberg majorizing and minorizing functions and use them to prove results on trigonometric approximation and to prove an n n -dimensional version of the Erdös-Turán inequality. Finally, an application is given to counting solutions of polynomial congruences.
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