Search results for: Alexandru Zaharescu

Items from 1 to 20 out of 104 results

article

Sondow’s conjecture, convergents to e, and p-adic analytic functions

Vicenţiu Paşol, Alexandru Zaharescu

Mathematische Zeitschrift > 2019 > 292 > 1-2 > 499-511

In their study of diophantine approximation of the exponential function in connection with Sondow’s Conjecture, Berndt et al. (Adv Math 348:1298–1331, 2013) have constructed certain p-adic functions arising from the sequence of convergents to the continued fraction of e. We solve an open problem posed in [2], more precisely we show that those p-adic functions are locally analytic (of minimal radius...

article

Partitions into kth powers of terms in an arithmetic progression

Bruce C. Berndt, Amita Malik, Alexandru Zaharescu

Mathematische Zeitschrift > 2018 > 290 > 3-4 > 1277-1307

G. H. Hardy and S. Ramanujan established an asymptotic formula for the number of unrestricted partitions of a positive integer, and claimed a similar asymptotic formula for the number of partitions into perfect kth powers, which was later proved by E. M. Wright. Recently, R. C. Vaughan provided a simpler asymptotic formula in the case $$k=2$$ k=2 . In this paper, we consider partitions into parts...

article

Rapid prototyping of geosynthetic interfaces: Investigation of peak strength using direct shear tests

Gary John Fowmes, Neil Dixon, Liwei Fu, Catalin Alexandru Zaharescu

Geotextiles and Geomembranes > 2017 > 45 > 6 > 674-687

Rapid prototyping offers a platform technology for investigations within the geosynthetics research and manufacturing sectors. This paper considers the application of rapid prototyping for the development of geosynthetic interfaces. The benefits and challenges of three rapid prototyping techniques (fused filament fabrication, selective laser sintering and laser thermal ablation) are considered and...

article

Exact evaluation of second moments associated with some families of curves over a finite field

Ravi Donepudi, Junxian Li, Alexandru Zaharescu

Finite Fields and Their Applications > 2017 > 48 > C > 331-355

Let Fq be the finite field with q elements. Given an N-tuple Q∈FqN, we associate with it an affine plane curve CQ over Fq. We consider the distribution of the quantity q−#Cq,Q where #Cq,Q denotes the number of Fq-points of the affine curve CQ, for families of curves parameterized by Q. Exact formulae for first and second moments are obtained in several cases when Q varies over a subset of FqN. Families...

article

The largest gap between zeros of entire L-functions is less than 41.54

Patrick Kühn, Nicolas Robles, Alexandru Zaharescu

Journal of Mathematical Analysis and Applications > 2017 > 449 > 2 > 1286-1301

Using suitable feasible pairs and convex combinations of Selberg minorant functions, the upper bound under GRH and the Ramanujan hypothesis on the largest gap between consecutive zeros of an entire L-function in Bober, Conrey, Farmer, Fujii, Koutsoliotas, Lemurell, Rubinstein and Yoshida [2] is improved from 45.3236 to 41.54. An application about nonexistence of certain entire L-functions is also...

article

Smooth $$L^2$$ L 2 distances and zeros of approximations of Dedekind zeta functions

Junxian Li, Maria Nastasescu, Arindam Roy, Alexandru Zaharescu

manuscripta mathematica > 2017 > 154 > 1-2 > 195-223

We consider a family of approximations of the Dedekind zeta function $$\zeta _K(s)$$ ζ K ( s ) of a number field $$K/\mathbb {Q}$$ K / Q . Weighted $$L^2$$ L 2 -norms of the difference of two such approximations of $$\zeta _K(s)$$ ζ K ( s ) are computed. We work with a weight which is a compactly supported smooth function. Mean square estimates for...

article

New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan

Bruce C. Berndt, Atul Dixit, Arindam Roy, Alexandru Zaharescu

Advances in Mathematics > 2017 > 304 > C > 809-929

The focus of this paper commences with an examination of three (not obviously related) pages in Ramanujan's lost notebook, pages 336, 335, and 332, in decreasing order of attention. On page 336, Ramanujan proposes two identities, but the formulas are wrong – each is vitiated by divergent series. We concentrate on only one of the two incorrect “identities,” which may have been devised to attack the...

article

A growth model based on the arithmetic Z-game

Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu

Chaos, Solitons & Fractals > 2016 > 91 > C > 136-147

We present an evolutionary self-governing model based on the numerical atomic rule Z(a,b)=ab/gcd(a,b)2, for a, b positive integers. Starting with a sequence of numbers, the initial generation Gin, a new sequence is obtained by applying the Z-rule to any neighbor terms. Likewise, applying repeatedly the same procedure to the newest generation, an entire matrix TGin is generated. Most often, this matrix,...

article

A generalization of the Schur–Siegel–Smyth trace problem

Kyle Pratt, George Shakan, Alexandru Zaharescu

Journal of Mathematical Analysis and Applications > 2016 > 436 > 1 > 489-500

Let α be a totally positive algebraic integer, and define its absolute trace to be Tr(α)deg(α), the trace of α divided by the degree of α. Elementary considerations show that the absolute trace is always at least one, while it is plausible that for any ϵ>0, the absolute trace is at least 2−ϵ with only finitely many exceptions. This is known as the Schur–Siegel–Smyth trace problem. Our aim in this...

article

Continuous automorphisms of transcendental closed subfields of $$\mathbb {C}_p$$ C p

Victor Alexandru, Marian Vâjâitu, Alexandru Zaharescu

Monatshefte für Mathematik > 2016 > 181 > 3 > 527-535

Given a prime number p we study the continuous automorphisms of transcendental closed subfields of $$\mathbb {C}_p$$ C p , the topological completion of the algebraic closure of the field of p-adic numbers.

article

Koshliakov kernel and identities involving the Riemann zeta function

Atul Dixit, Nicolas Robles, Arindam Roy, Alexandru Zaharescu

Journal of Mathematical Analysis and Applications > 2016 > 435 > 2 > 1107-1128

Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions Jz(x), Yz(x) and Kz(x) are studied. Interesting special cases of these identities are derived, one of which is connected to a well-known transformation due to Ramanujan, and Guinand.

article

Riesz-type criteria and theta transformation analogues

Atul Dixit, Arindam Roy, Alexandru Zaharescu

Journal of Number Theory > 2016 > 160 > C > 385-408

We give character analogues of a generalization of a result due to Ramanujan, Hardy and Littlewood, and provide Riesz-type criteria for Riemann Hypotheses for the Riemann zeta function and Dirichlet L-functions. We also provide analogues of the general theta transformation formula and of recent generalizations of the transformation formulas of W.L. Ferrar and G.H. Hardy for real primitive Dirichlet...

article

Twisted second moments of the Riemann zeta-function and applications

Nicolas Robles, Arindam Roy, Alexandru Zaharescu

Journal of Mathematical Analysis and Applications > 2016 > 434 > 1 > 271-314

In order to compute a twisted second moment of the Riemann zeta-function, two different mollifiers, each being a combination of two different Dirichlet polynomials, were introduced separately by Bui, Conrey, and Young, and by Feng. In this article we introduce a mollifier which is a combination of four Dirichlet polynomials of different shapes. We provide an asymptotic result for the twisted second...

article

On the correlation of families of pseudorandom sequences of k symbols

Kit-Ho Mak, Alexandru Zaharescu

Acta Arithmetica > 2016 > 174 > 3 > 199-215

In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.

article

Some identities involving convolutions of Dirichlet characters and the Möbius function

Arindam Roy, Alexandru Zaharescu, Mohammad Zaki

Proceedings - Mathematical Sciences > 2016 > 126 > 1 > 21-33

In this paper, we present some identities involving convolutions of Dirichlet characters and the Möbius function, which are related to a well known identity of Ramanujan, Hardy and Littlewood.

article

Pair correlation of fractional parts derived from rational valued sequences, II

Sneha Chaubey, Melinda Lanius, Alexandru Zaharescu

Journal of Number Theory > 2016 > 158 > C > 151-164

A rational valued vector sequence x→, for some fixed k and r∈N, is a map x→:Nk→Qr. In the present paper, we complement the results of [3] with a discussion on rational valued vector sequences. We investigate the pair correlation function for the fractional parts of sequences t→⋅x→, where x→ is a rational valued vector sequence and t→∈Rr. We offer a new class of sequences x→ whose pair correlation...

article

Weighted divisor sums and Bessel function series, V

Bruce C. Berndt, Sun Kim, Alexandru Zaharescu

Journal of Approximation Theory > 2015 > 197 > Complete > 101-114

Let r2(n) denote the number of representations of n as a sum of two squares. Finding the precise order of magnitude for the error term in the asymptotic formula for ∑n≤xr2(n) is known as the circle problem. Next, let d(n) denote the number of positive divisors of n. Determining the exact order of magnitude of the error term associated with the asymptotic formula for ∑n≤xd(n) is the divisor problem...

article

Pair correlation of fractional parts derived from rational valued sequences

Sneha Chaubey, Melinda Lanius, Alexandru Zaharescu

Journal of Number Theory > 2015 > 151 > Complete > 147-158

We investigate the pair correlation of the sequence of fractional parts of αxn, n∈N, where xn is rational valued and α is a real number. As examples, we offer two classes of sequences xn whose pair correlation behaves as that of random sequences for almost all real numbers α. First, sequences of the form xn=an/bn where an is lacunary and bn satisfies a certain growth condition. Second, sequences of...

article

Ramanujan–Hardy–Littlewood–Riesz phenomena for Hecke forms

Atul Dixit, Arindam Roy, Alexandru Zaharescu

Journal of Mathematical Analysis and Applications > 2015 > 426 > 1 > 594-611

We generalize a result of Ramanujan, Hardy and Littlewood to the setting of primitive Hecke forms, which interestingly exhibits faster convergence than in the initial case of the Riemann zeta function. We also provide a criterion in the spirit of Riesz for the Riemann Hypothesis for the associated L-functions.

article

Zeros of combinations of the Riemann ξ-function on bounded vertical shifts

Atul Dixit, Nicolas Robles, Arindam Roy, Alexandru Zaharescu

Journal of Number Theory > 2015 > 149 > Complete > 404-434

In this paper we consider a series of bounded vertical shifts of the Riemann ξ-function. Interestingly, although such functions have essential singularities, infinitely many of their zeros lie on the critical line. We also generalize some integral identities associated with the theta transformation formula and some formulae of G.H. Hardy and W.L. Ferrar in the context of a pair of functions reciprocal...

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INFONA - science communication portal

Search results for: Alexandru Zaharescu

Sondow’s conjecture, convergents to e, and p-adic analytic functions

Partitions into kth powers of terms in an arithmetic progression

Rapid prototyping of geosynthetic interfaces: Investigation of peak strength using direct shear tests

Exact evaluation of second moments associated with some families of curves over a finite field

The largest gap between zeros of entire L-functions is less than 41.54

Smooth $$L^2$$ L 2 distances and zeros of approximations of Dedekind zeta functions

New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan

A growth model based on the arithmetic Z-game

A generalization of the Schur–Siegel–Smyth trace problem

Continuous automorphisms of transcendental closed subfields of $$\mathbb {C}_p$$ C p

Koshliakov kernel and identities involving the Riemann zeta function

Riesz-type criteria and theta transformation analogues

Twisted second moments of the Riemann zeta-function and applications

On the correlation of families of pseudorandom sequences of k symbols

Some identities involving convolutions of Dirichlet characters and the Möbius function

Pair correlation of fractional parts derived from rational valued sequences, II

Weighted divisor sums and Bessel function series, V

Pair correlation of fractional parts derived from rational valued sequences

Ramanujan–Hardy–Littlewood–Riesz phenomena for Hecke forms

Zeros of combinations of the Riemann ξ-function on bounded vertical shifts

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