Results 21 to 30 of about 198,499,059 (216)
Kaplansky's ternary quadratic form
International Journal of Mathematics and Mathematical Sciences, 2001 This paper proves that if N is a nonnegative eligible integer, coprime to 7, which is not of the form x2+y2+7z2, then N is square-free. The proof is modelled on that of a similar theorem by Ono and Soundararajan, in which relations between the number of ...
James Kelley
doaj +1 more source
On the Vanishing of TwistedL-Functions of Elliptic Curves [PDF]
Experimental Mathematics, 2004 Let E be an elliptic curve over q with L-function {\small $L_E(s)$}. We use the random matrix model of Katz and Sarnak to develop a heuristic for the frequency of vanishing of the twisted L-functions {\small $L_E(1, \chi)$}, as {\small $\chi$} runs over the Dirichlet characters of order 3 (cubic twists).
David, Chantal +2 more
openaire +2 more sources
The Scientific World Journal, 2016 Growing attractiveness of Mobile Ad Hoc Networks (MANETs), its features, and usage has led to the launching of threats and attacks to bring negative consequences in the society.
Anitha Veerasamy +3 more
doaj +1 more source
Iwasawa theory for modular forms at supersingular primes [PDF]
, 2010 Let f=\sum a_nq^n be a normalised eigen-newform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q.
Antonio Lei
core +2 more sources
Algebraic divisibility sequences over function fields [PDF]
, 2011 In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields ...
Mahe, Valery +14 more
core +2 more sources
Design and Analysis of Power-function-sine Flexure Hinges
Jixie chuandong, 2023 In this study, a new type of power-function-sine flexure hinge is proposed. The calculation formula of compliance and rotation accuracy of the flexure hinge is derived by using Castigliano's second theorem.
Li Jiabiao +5 more
doaj
Estimates for $L$-Functions Associated with Some Elliptic Curves
Rocky Mountain Journal of Mathematics, 1996 Let \(E_D\) be either of the curves \(y^2= x^3-Dx\) or \(y^2=X^3+ D\), and let \(N\) be the conductor of \(E_D\). Let \(L_D(s)\) be the \(L\)-function of \(E_D\), and let \(L^{(2)}_D(s)\) be its symmetric square. It is proved that \[ L_D\Biggl(\frac{3}{2}\Biggr) \ll\log^cN\quad\text{and}\quad \log^{-c}N\ll L^{(2)}_D\Biggl(\frac{3}{2}\Biggr)\ll \log^cN,
Chamizo, Fernando, Iwaniec, Henryk
openaire +3 more sources
The p-Adic L-Functions of Modular Elliptic Curves [PDF]
, 2001 The arithmetic theory of elliptic curves enters the new century with some of its major secrets intact. Most notably, the Birch and Swinnerton-Dyer conjecture, which relates the arithmetic of an elliptic curve to the analytic behaviour of its associated L-series, is still unproved in spite of important advances in the last decades, some of which are ...
M. Bertolini, H. Darmon
openaire +2 more sources
Maximal Galois Group of L-Functions of Elliptic Curves [PDF]
International Mathematics Research Notices, 2009 We give a quantitative version of a result due to N. Katz about L-functions of elliptic curves over function fields over finite fields. Roughly speaking, Katz's Theorem states that, on average over a suitably chosen algebraic family, the L-function of an elliptic curve over a function field becomes "as irreducible as possible" when seen as a polynomial
openaire +2 more sources
An elliptic curve test of the L-Functions Ratios Conjecture
Journal of Number Theory, 2011 We compare the L-Function Ratios Conjecture's prediction with number theory for the family of quadratic twists of a fixed elliptic curve with prime conductor, and show agreement in the 1-level density up to an error term of size X^{-(1-sigma)/2} for test functions supported in (-sigma, sigma); this gives us a power-savings for σ<1.
Huynh, Duc Khiem +2 more
openaire +2 more sources