Results 41 to 50 of about 990 (79)
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
Resultant and conductor of geometrically semi-stable self maps of the projective line over a number field or function field [PDF]
, 2010 We study the minimal resultant divisor of self-maps of the projective line over a number field or a function field and its relation to the conductor. The guiding focus is the exploration of a dynamical analog to Theorem 1.1, which bounds the degree of ...
L. Szpiro, Michael Tepper, P. Williams
semanticscholar +1 more source
On the largest element in D(n)-quadruples
, 2019 Let $n$ be a nonzero integer. A set of nonzero integers $\{a_1,\ldots,a_m\}$ such that $a_ia_j+n$ is a perfect square for all $1\leq ...
Dujella, Andrej, Petričević, Vinko
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More around Pythagore from ancient to modern times
, 2013 This work deals with the history around the ”Pythagorean Theorem“ and the ”Pythagorean Number Triples“ from 2200 B.C. until today. Special emphasis is done on china, including early applications.
A. Faessler, Xi Tu
semanticscholar +1 more source
Sums of two biquadrates and elliptic curves of rank $\geq 4$ [PDF]
, 2012 If an integer $n$ is written as a sum of two biquadrates in two different ways, then the elliptic curve $y^2=x^3-nx$ has rank $\geq 3$. If moreover $n$ is odd and the parity conjecture is true, then it has even rank $\geq 4$.
Izadi, F. A., Khoshnam, F., Nabardi, K.
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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
, 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
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
On a Conjecture of Cai-Zhang-Shen for Figurate Primes
, 2019 A conjecture of Cai-Zhang-Shen for figurate primes says that every integer n > 1 is the sum of two figurate primes. In this paper we give respectively equivalent propositions to the conjecture in the cases of even and odd integers and then confirm the ...
Niu, Pengcheng
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