8 papers
Local Factors in the BSD Conjecture: A Unified Statistical View
David Kurniadi Angdinata, Kenny Lau, Ken Ono +2
For elliptic curves in short Weierstrass form \[ E=E(a_4,a_6): y^2=x^3+a_4x+a_6, \] we derive a multivariable Euler product generating function which encodes the Tam…
Tamagawa numbers and torsion of elliptic curves over function fields
David Kurniadi Angdinata, Mentzelos Melistas
We study the divisibilities of Tamagawa numbers of elliptic curves over global function fields in terms of their torsion subgroups $ E(K)_{\operatorname{tors}}…
ABC implies that Ramanujan's tau function misses almost all primes
David Kurniadi Angdinata, Evan Chen, Chris Cummins +21
Lehmer conjectured that Ramanujan's tau-function never vanishes. In a related direction, a folklore conjecture asserts that infinitely many primes arise as absolute values of Raman…
On the paucity of lattice triangles
David Kurniadi Angdinata, Evan Chen, Ken Ono +3
A rational triangle (one whose angles are rational multiples of ) unfolds to a translation surface . The lattice triangle problem asks to classify those for which…
Computing L-functions of -adic representations of global function fields
David Kurniadi Angdinata
The L-function of an almost everywhere unramified -adic representation of a global function field is known to be a rational function in…
Algebraicity of Artin--Hasse--Weil L-series over global function fields
David Kurniadi Angdinata
We prove an analogue of Deligne's period conjecture for the special value of the L-function of an abelian variety over a global function field twisted by an Artin representation. W…
L-values of elliptic curves twisted by cubic characters
David Kurniadi Angdinata
Given a rational elliptic curve of analytic rank zero, its L-function can be twisted by an even primitive Dirichlet character of order , and in many cases its assoc…
An Elementary Formal Proof of the Group Law on Weierstrass Elliptic Curves in any Characteristic
David Kurniadi Angdinata, Junyan Xu
Elliptic curves are fundamental objects in number theory and algebraic geometry, whose points over a field form an abelian group under a geometric addition law. Any elliptic curve…