Results 41 to 50 of about 12,228,153 (333)
Teaching Arithmetic to Small Transformers [PDF]
arXiv.org, 2023 Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction ...
Nayoung Lee +4 more
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Inequalities between some arithmetic functions, II [PDF]
Notes on Number Theory and Discrete MathematicsAs a continuation of Part I (see [1]), we offer new inequalities for classical arithmetic functions such as the Euler's totient function, the Dedekind's psi function, the sum of the positive divisors function, the number of divisors function, extended ...
Krassimir Atanassov +2 more
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On certain inequalities for φ, ψ, σ and related functions, III [PDF]
Notes on Number Theory and Discrete MathematicsWe obtain generalizations of certain results from [2] and [4]. The unitary variants are also considered. Some new arithmetic functions and their inequalities are also considered.
József Sándor, Karol Gryszka
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Representation zeta functions of compact p-adic analytic groups and arithmetic groups [PDF]
, 2013 We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups.
Onn, Uri +3 more
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Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The set Set(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [4], some arithmetic functions and arithmetic operators of a modal type are defined over the elements of Set(n).
Krassimir Atanassov
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Arithmetic functions in short intervals and the symmetric group [PDF]
Algebra & Number Theory, 2016 We consider the variance of sums of arithmetic functions over random short intervals in the function field setting. Based on the analogy between factorizations of random elements of $\mathbb{F}_q[T]$ into primes and the factorizations of random ...
Brad Rodgers
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Graphical shell for constructing user-entered arithmetic functions
Adaptivni Sistemi Avtomatičnogo Upravlinnâ, 2023 The article has a relevant topic in the scientific and practical aspect development of a graphical shell of a software application for constructing functions of two variables entered by the user.
V. Smolij, N. Smolij, О. Lisovychenko
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IEEE International Conference on Application-Specific Systems, Architectures, and Processors, 2019 Stochastic computing (SC) has emerged as a potential alternative to binary computing for a number of low-power embedded systems, DSP, neural networks and communications applications.
Tieu-Khanh Luong +3 more
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Recurrence relations for polynomials obtained by arithmetic functions
International Journal of Number Theory, 2019 Families of polynomials associated to arithmetic functions [Formula: see text] are studied. The case [Formula: see text], the divisor sum, dictates the non-vanishing of the Fourier coefficients of powers of the Dedekind eta function.
B. Heim, F. Luca, M. Neuhauser
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Correlations of sums of two squares and other arithmetic functions in function fields [PDF]
, 2017 We investigate a function field analogue of a recent conjecture on autocorrelations of sums of two squares by Freiberg, Kurlberg and Rosenzweig, which generalizes an older conjecture by Connors and Keating.
L. Bary‐Soroker, Arno Fehm
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