Results 11 to 20 of about 491,257 (81)
Additive Number Theory via Approximation by Regular Languages [PDF]
International Conference on Developments in Language Theory, 2018 We prove some new theorems in additive number theory, using novel techniques from automata theory and formal languages. As an example of our method, we prove that every natural number [Formula: see text] is the sum of at most three natural numbers whose ...
J. Bell, T. Lidbetter, J. Shallit
semanticscholar +1 more source
Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects [PDF]
Communications in Number Theory and Physics, 2016 We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a ...
Imma G'alvez-Carrillo +2 more
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Characteristic ideals and Selmer groups [PDF]
, 2014 Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let $\calf/F$ be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally ramified, we define
Bandini, Andrea +2 more
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Twisted character of a small representation of GL(4)
, 2006 We compute by a purely local method the (elliptic) twisted by transpose-inverse character \chi_{\pi_Y} of the representation \pi_Y=I_{(3,1)}(1_3x\chi_Y) of G=GL(4,F), where F is a p-adic field, p not 2, and Y is an unramified quadratic extension of F ...
Flicker, Yuval Z., Zinoviev, Dmitrii
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Proof of a congruence for harmonic numbers conjectured by Z.-W. Sun
, 2012 For a positive integer $n$ let $H_n=\sum_{k=1}^{n}1/k$ be the $n$th harmonic number. In this note we prove that for any prime $p\ge 7$, $$ \sum_{k=1}^{p-1}\frac{H_k^2}{k^2} \equiv4/5pB_{p-5}\pmod{p^2}, $$ which confirms the conjecture recently ...
Mestrovic, Romeo
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IEEE potentials, 1989 Number theory, an abstract branch of mathematics that deals with relationships between whole numbers, has provided highly useful answers to numerous real-world problems.
Don Redmond
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Numeration Systems: A Link between Number Theory and Formal Language Theory [PDF]
International Conference on Developments in Language Theory, 2010 We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions.
M. Rigo
semanticscholar +1 more source
Kummer theory for number fields and the reductions of algebraic numbers
International Journal of Number Theory, 2019 For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov–Ribet method) of the fact that if [Formula: see text] is a finitely generated and ...
Antonella Perucca, Pietro Sgobba
semanticscholar +1 more source
Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average
, 2007 We prove that the set of Farey fractions of order $T$, that is, the set $\{\alpha/\beta \in \Q : \gcd(\alpha, \beta) = 1, 1 \le \alpha, \beta \le T\}$, is uniformly distributed in residue classes modulo a prime $p$ provided $T \ge p^{1/2 +\eps}$ for any ...
Cojocaru, A. C., Shparlinski, I. E.
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Discretisation for odd quadratic twists [PDF]
, 2005 The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction.
Conrey, J. Brian +3 more
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