The Ljunggren equation revisited
We study the Ljunggren equation Y² + 1 = 2X⁴ using the "multiplication by 2" method of Chabauty.
The local Jacquet-Langlands correspondence via Fourier analysis
Let be a locally compact non-Archimedean field, and let be a division algebra of dimension 4. The Jacquet-Langlands correspondence provides a bijection between smooth irreducible representations of of dimension and irreducible cuspidal representations of . We present a new construction of this bijection in which the preservation of epsilon factors is automatic. This is done by constructing a family of pairs , where is an order and is a finite-dimensional representation of a certain...
The local lifting problem for actions of finite groups on curves
Let be an algebraically closed field of characteristic . We study obstructions to lifting to characteristic the faithful continuous action of a finite group on . To each such a theorem of Katz and Gabber associates an action of on a smooth projective curve over . We say that the KGB obstruction of vanishes if acts on a smooth projective curve in characteristic in such a way that and have the same genus for all subgroups . We determine for which the KGB obstruction...
The local monodromy as a generalized algebraic correspondence (with an appendix by Spencer Bloch).
The localisation of primes in arithmetic progressions of irrational modulus
A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.
The Logarithm of the Dedekind n-Function.
The logarithm of the Siegel function
The lonely runner with seven runners.
The lowest term of the Schottky modular form.
The lowest zero of sections of the zeta function.
The L-Theory of Laurent extensions and genus 0 function fields.
The Lucas congruence for Stirling numbers of the second kind
0. Introduction. The numbers introduced by Stirling in 1730 in his Methodus differentialis [11], subsequently called “Stirling numbers” of the first and second kind, are of the greatest utility in the calculus of finite differences, in number theory, in the summation of series, in the theory of algorithms, in the calculation of the Bernstein polynomials [9]. In this study, we demonstrate some properties of Stirling numbers of the second kind similar to those satisfied by binomial coefficients; in...
The Lvov years of Wacław Sierpiński
An account is given of Sierpiński's activity in Lvov (1908-1918) interrupted by World War I.
The Maap space on the half-plane of Cayley numbers of degree two.
The Maaß Space and Hecke Operators.
The Maaß space for Cayley numbers.
The Maaß spaces on the Hermitian half-space of degree 2.
The Maaß-Space on the Half-Space of Quaternions of Degree 2.
The Mahler measure of dihedral extensions
The "main conjectures" of Iwasawa theory for imaginary quadratic fields.