Papers 4832

1 page of 484 pages (4,832 results)

#1Andrew N.W. HoneH-Index: 28

#2Juan L. VaronaH-Index: 15

#1Jean-Marc DeshouillersH-Index: 14

#2Pramod EyyunniH-Index: 2

Last. Sanoli GunH-Index: 9

view all 3 authors...

Assuming the validity of Dickson's conjecture, we show that the set V of values of the Euler's totient function φ contains arbitrarily large arithmetic progressions with common difference 4. This leads to the question of proving unconditionally that this set V has a positive upper Banach density.

A Piatetski-Shapiro sequence with exponent \alphais a sequence of integer parts of n^\alpha(n = 1,2,\ldots)with a non-integral \alpha > 0 We let \mathrm{PS}(\alpha)denote the set of those terms. In this article, we study the set of \alphaso that the equation ax + by = czhas infinitely many pairwise distinct solutions (x,y,z) \in \mathrm{PS}(\alpha)^3 and give a lower bound for its Hausdorff dimension. As a corollary, we find uncountably many \alpha > 2such that $\mathr...

#1Florian BreuerH-Index: 10

#2Fabien PazukiH-Index: 6

Last. Mahefason Heriniaina RazafinjatovoH-Index: 1

view all 3 authors...

We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular polynomials attached to Drinfeld modules.

#1Jaitra ChattopadhyayH-Index: 2

#2S. MuthukrishnanH-Index: 26

Let k \geq 1be a cube-free integer with k \equiv 1 \pmod {9}and \gcd(k, 7\cdot 571)=1 In this paper, we prove the existence of infinitely many triples of imaginary quadratic fields \mathbb{Q}(\sqrt{d}) \mathbb{Q}(\sqrt{d+1})and \mathbb{Q}(\sqrt{d+k^2})with d \in \mathbb{Z}such that the class number of each of them is divisible by 3 This affirmatively answers a weaker version of a conjecture of Iizuka \cite{iizuka-jnt}.

#1Daniele BartoliH-Index: 15

#2Maria MontanucciH-Index: 9

Last. Giovanni ZiniH-Index: 10

view all 3 authors...

In this article we explicitly determine the structure of the Weierstrass semigroups H(P)for any point Pof the Suzuki curve \mathcal{S}_q As the point Pvaries, exactly two possibilities arise for H(P) one for the \mathbb{F}_qrational points (already known in the literature), and one for all remaining points. For this last case a minimal set of generators of H(P)is also provided. As an application, we construct dual one-point codes from an \mathbb{F}_{q^4}\setminus\fqpoint ...

#1Borys KucaH-Index: 1

#1Clemens FuchsH-Index: 11

#2Sebastian HeintzeH-Index: 2

We are interested in solutions of a norm form equation that takes values in a given multi-recurrence. We show that among the solutions there are only finitely many values in each component which lie in the given multi-recurrence unless the recurrence is of precisely described exceptional shape. This gives a variant of the question on arithmetic progressions in the solution set of norm form equations.

On the signed Selmer groups of congruent elliptic curves with semistable reduction at all primes above p

#1Suman AhmedH-Index: 2

#2Meng Fai LimH-Index: 5

Let pbe an odd prime. We attach appropriate signed Selmer groups to an elliptic curve E where Eis assumed to have semistable reduction at all primes above p We then compare the Iwasawa \lambdainvariants of these signed Selmer groups for two congruent elliptic curves over the cyclotomic \mathbb{Z}_pextension in the spirit of Greenberg-Vatsal and B. D. Kim. As an application of our comparsion formula, we show that if the pparity conjecture is true for one of the congruent elli...

12345678910