Explicit form of the modular equation.
Explicit forms of Kummer's complementary theorems to his law of quintic reciprocity.
Explicit formulae of Siegel Eisenstein series.
Explicit Formulas and Asymptotic Expansions for Certain Mean Square of Hurwitz Zeta-Functions.
Explicit formulas for Bernoulli and Euler numbers.
Explicit formulas for strong Davenport pairs
Explicit formulas for the constituent matrices. Application to the matrix functions
We present a constructive procedure for establishing explicit formulas of the constituents matrices. Our approach is based on the tools and techniques from the theory of generalized Fibonacci sequences. Some connections with other results are supplied. Furthermore,we manage to provide tractable expressions for the matrix functions, and for illustration purposes we establish compact formulas for both the matrix logarithm and the matrix pth root. Some examples are also provided.
Explicit formulas for the eigenvalues of Hecke operators
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.