On Eisenstein series with characters and Dedekind sums
On Eisenstein series with characters and the values of Dirichlet L-functions
On Eisenstein's problem
On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields
A large number of papers have contributed to determining the structure of the tame kernel of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for have been made very explicit by Qin Hourong in terms of the indefinite quadratic form x² - 2y² (see [7], [8]). We have made a successful effort, for quadratic number fields F = ℚ (√(±p₁p₂)), to characterize in terms of positive definite binary quadratic forms,...
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...
On elementary lower bounds for the partition function.
On Elkies subgroups of -torsion points in elliptic curves defined over a finite field
As a subproduct of the Schoof-Elkies-Atkin algorithm to count points on elliptic curves defined over finite fields of characteristic , there exists an algorithm that computes, for an Elkies prime, -torsion points in an extension of degree at cost bit operations in the favorable case where .We combine in this work a fast algorithm for computing isogenies due to Bostan, Morain, Salvy and Schost with the -adic approach followed by Joux and Lercier to get an algorithm valid without any limitation...
On elliptic curves and random matrix theory
Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.
On elliptic curves in characteristic 2 with wild additive reduction
On elliptic diophantine equations that defy Thue's method: The case of the Ochoa curve.
On elliptic Galois representations and genus-zero modular units
Given an odd prime and a representation of the absolute Galois group of a number field onto with cyclotomic determinant, the moduli space of elliptic curves defined over with -torsion giving rise to consists of two twists of the modular curve . We make here explicit the only genus-zero cases and , which are also the only symmetric cases: for or , respectively. This is done by studying the corresponding twisted Galois actions on the function field of the curve, for which...
On elliptic units and class number of a certain dihedral extension of degree 2l
On Elliptic Units and Class Number of a Certain Non-Galois Number Field.
On embedding numbers into quaternion orders.
On endo-lifting
On entire modular forms of half-integral weight on the congruence subgroup .
On entry 8 of Chapter 15 of Ramanujan's Notebook II
On Epstein's Zeta-function.
On equal values of power sums
On equation in S-units and the Thue-Mahler equation.