# 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

**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 ...

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### On a second conjecture of Stolarsky: the sum of digits of polynomial values

**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**...

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### On a conjecture of Dekking : The sum of digits of even numbers

**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

**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

**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

**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

**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

**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

**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

**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

**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

9

### The optimality of the Bounded Height Conjecture

**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 $n!+ 2^n-1$

**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

**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

**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

**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

15

### Some Results About a Conjecture on Identifying Codes in Complete Suns

**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

**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 ...

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