Haut PDF On Gelfond’s conjecture about the sum of digits of prime numbers
On Gelfond’s conjecture about the sum of digits of prime numbers
... Abstract. The goal of this paper is to outline the proof of a conjecture of Gelfond [6] (1968) in a recent work in collaboration with Christian Mauduit [11] concerning ...
9
On a second conjecture of Stolarsky: the sum of digits of polynomial values
... and the variance of the values of the sum-of-digits function (see [1] or ...use the letter p to refer to a prime number, and use π(N ) for the ...
10
On a conjecture of Dekking : The sum of digits of even numbers
... determined the optimal exponent λ in the error term in Gelfond’s asymptotic formula when q = m = 2, and Shparlinski [10] showed that in this case it can be arbitrarily small for sufficiently large primes ...
9
On the number of prime factors of summands of partitions
... γ of n, about half of the parts have even and half of them odd number of prime factors, ...e., the Liouville function λ(N ) = (−1) Ω(N ) assumes the values ...
16
Some improvements of the S-adic conjecture
... consequence of Proposition 2.1 is that we cannot have an upper bound on the complexity of S-adic sequences like the one we have for fixed points of substitutions (see ...satisfying ...
25
Measurement of the relative branching fractions of $B^+ \to h^+h^{\prime +}h^{\prime -}$ decays
... distributions of the (top) B + → K + π + π − and (bottom) B + → π + π + π − candidates compared to the results of the simultaneous fit with (left) linear and (right) logarithmic y-axis ...
29
Two generalizations of the PRV conjecture
... on the saturation question for semigroups LR(G, G × G) (see ...ν of T . The intersection of LR(G, G × G) with X(T ) ⊗ Q × {µ} × {ν} is a polytope P (µ, ν) (namely, a moment ...polytope). ...
23
A step toward the Bermond-Thomassen conjecture about disjoint cycles in digraphs
... cycles of D. 4 Proof of Theorem 2 Our goal in this section is to establish Theorem ...that the statement of the theorem is false, and consider a counter-example with the minimum ...
21
Automaticity of the sequence of the last nonzero digits of $n!$ in a fixed base
... Basics of automatic sequences In this section we will give a short summary of topics from automatic sequence theory that we will be using ...If the reader is interested in getting more insight into ...
10
Prime divisors of the Lagarias sequence
... have the fundamental equivalence p divides xn 4=~’ -c/c = (a/a)n EO/pO Here 0 is the ring of integers in the field generated by the roots of f ...is the ring Z if f has ...
12
On the prime density of Lucas sequences
... From the law of quadratic reciprocity one deduces that for odd D, (D/p) = 1 if and only if p - 4D) for a set of odd ¡3 (this result was already conjectured by ...this, the supplementary law ...
12
Computing one million digits of racine de 2
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ...
9
The optimality of the Bounded Height Conjecture
... principally the optimality of the Bounded Height Conjecture, stated by Bombieri, Masser and Zannier [2] and proven by Habegger ...clarify the assumption on the varieties, un- ...
17
On the largest prime factor of $n!+ 2^n-1$
... de Bordeaux 17 (2005), 859–870 On the largest prime factor of n! + 2 n − 1 par Florian LUCA et Igor E. SHPARLINSKI R´ esum´ e. Pour un entier n ≥ 2, notons P (n) le plus grand facteur premier de n. ...
13
Minimizing the sum of many rational functions
... controller of a linear system subject to parametric ...but the application of our techniques to computer vision and systems control will be described ...on the optimum. In this paper we were ...
28
The Multiplicative Power of Consensus Numbers
... class of decision tasks called colorless tasks (those are the tasks where, if a process decides a value, any other process is allowed to decide the very same value), BG simulation characterizes ...
18
On the binary expansions of algebraic numbers
... 1.88 of [10], which asks for a fast ...emerged the field of “experimental mathematics,” wherein one uses high-precision numerical relations such as linear reduction to suggest exact algebraic ...
33
Approximability of the Subset Sum Reconfiguration Problem
... We show in Section 3.1 that the problem can be optimally solved in polynomial time if A contains only large items; in this case, the number of packings and hence the number of vertices i[r] ...
15
Some Results About a Conjecture on Identifying Codes in Complete Suns
... (G) the minimum cardinality of an identifying code in ...are the locating-dominating codes, which are less de- manding: a subset C ⊆ V is a locating-dominating code (LD code for short) if the ...
19
The prime divisors of the number of points on abelian varieties
... If the condition K(A[`]) ⊆ K(A 0 [`]) holds for infinitely many prime numbers ` then A, A 0 are ...Note, the condition K(A[`]) = K(A 0 [`]) for every prime number ` does not in general ...
11
