Results 31 to 40 of about 920 (62)
Reduction of CM elliptic curves and modular function congruences [PDF]
, 2005 We study congruences of the form F(j(z)) | U(p) = G(j(z)) mod p, where U(p) is the p-th Hecke operator, j is the basic modular invariant 1/q+744+196884q+... for SL2(Z), and F,G are polynomials with integer coefficients.
Elkies, Noam D., Ono, Ken, Yang, Tonghai
core +2 more sources
Constructing families of moderate-rank elliptic curves over number fields [PDF]
, 2017 We generalize a construction of families of moderate rank elliptic curves over $\mathbb{Q}$ to number fields $K/\mathbb{Q}$. The construction, originally due to Steven J.
Mehrle, David +4 more
core
, 2008 The first part of the paper gives a new proof of self-duality for Selmer groups: if A is an abelian variety over a number field K, and F/K is a Galois extension with Galois group G, then the Q_pG-representation naturally associated to the p-infinity ...
Grothendieck +6 more
core +2 more sources
When are Multiples of Polygonal Numbers again Polygonal Numbers?
, 2018 Euler showed that there are infinitely many triangular numbers that are three times other triangular numbers. In general, it is an easy consequence of the Pell equation that for a given square-free m > 1, the relation P=mP' is satisfied by infinitely ...
Chahal, Jasbir S. +2 more
core +1 more source
The yoga of the Cassels-Tate pairing
, 2007 Cassels has described a pairing on the 2-Selmer group of an elliptic curve which shares some properties with the Cassels-Tate pairing.
Brown +7 more
core +2 more sources
On the Mordell-Weil lattice of y 2 = x 3 + b x + t 3 n + 1 in characteristic 3. [PDF]
Res Number Theory, 2022 Leterrier G.
europepmc +1 more source
Orienteering with One Endomorphism. [PDF]
Mathematica (N Y), 2023 Arpin S +5 more
europepmc +1 more source
The Lang-Trotter Conjecture on Average
, 2006 For an elliptic curve $E$ over $\ratq$ and an integer $r$ let $\pi_E^r(x)$ be the number of primes $p\le x$ of good reduction such that the trace of the Frobenius morphism of $E/\fie_p$ equals $r$.
Baier, Stephan
core +1 more source
, 2019 For an elliptic curve $E$ over $K$, the Birch and Swinnerton-Dyer conjecture predicts that the rank of Mordell-Weil group $E(K)$ is equal to the order of the zero of $L(E_{/ K},s)$ at $s=1$.
Morita, Kazuma
core
Anti-PD1 'SHR-1210' aberrantly targets pro-angiogenic receptors and this polyspecificity can be ablated by paratope refinement. [PDF]
MAbs, 2019 Finlay WJJ +3 more
europepmc +1 more source