Explicit formulas for the Fourier coefficients.
Explicit formulas for the Fourier coefficients of Jacobi and elliptic modular forms.
Explicit geodesic flow-invariant distributions using -representation ladders.
Explicit global function fields over the binary field with many rational places
Explicit Hecke series for symplectic group of genus 4
Shimura conjectured the rationality of the generating series for Hecke operators for the symplectic group of genus . This conjecture was proved by Andrianov for arbitrary genus , but the explicit expression was out of reach for genus higher than 3. For genus , we explicitly compute the rational fraction in this conjecture. Using formulas for images of double cosets under the Satake spherical map, we first compute the sum of the generating series, which is a rational fraction with polynomial coefficients....
Explicit incidence bounds over general finite fields
Explicit inverse of the Pascal matrix plus one.
Explicit local heights.
Explicit lower bounds for
Explicit lower bounds for linear forms in two logarithms
We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in [10]. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around instead of .
Explicit moduli for curves of genus 2 with real multiplication by ℚ(√5)
1. Motivation. Let J₀(N) denote the Jacobian of the modular curve X₀(N) parametrizing pairs of N-isogenous elliptic curves. The simple factors of J₀(N) have real multiplication, that is to say that the endomorphism ring of a simple factor A contains an order in a totally real number field of degree dim A. We shall sometimes abbreviate "real multiplication" to "RM" and say that A has maximal RM by the totally real field F if A has an action of the full ring of integers of F. We say that a...
Explicit reciprocity laws for Lubin-Tate modules.
Explicit reciprocity laws on relative Lubin-Tate groups
Explicit reduction theory for Siegel modular threefolds.
Explicit Representations of Dirichlet Approximations.
Explicit Selmer groups for cyclic covers of ℙ¹
For any abelian variety J over a global field k and an isogeny ϕ: J → J, the Selmer group is a subgroup of the Galois cohomology group , defined in terms of local data. When J is the Jacobian of a cyclic cover of ℙ¹ of prime degree p, the Selmer group has a quotient by a subgroup of order at most p that is isomorphic to the ‘fake Selmer group’, whose definition is more amenable to explicit computations. In this paper we define in the same setting the ‘explicit Selmer group’, which is isomorphic...
Explicit solution of a class of quartic Thue equations
Explicit upper bounds for |L(1,χ)| for primitive even Dirichlet characters
Explicit upper bounds for |L(1,χ)| when χ(3) = 0
Let χ be a primitive Dirichlet character of conductor q and denote by L(z,χ) the associated L-series. We provide an explicit upper bound for |L(1,χ)| when 3 divides q.
Explicit upper bounds for the average order of and application to class number.