Function fields of certain arithmetic curves and application
Function Fields of Quadratic Forms.
Function fields with 3-rank at least 2
Function fields with class number indivisible by a prime ℓ
Function Fileds of Pfister Forms.
Function minimum associated to a congruence on integral n-tuple space.
Functional equation for partial zeta functions twisted by additive characters
Functional equation satisfied by certain -functions
Functional equations for Hurwitz series and partial zeta functions of orders.
Functional equations for L-functions of arithmetic orders.
Functional equations for zeta functions of non-Gorenstein orders in global fields.
Functions and polynomials ()
Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality
We prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma-Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. We also discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure...
Functions of slow increase and integer sequences.
Functorial concepts of complexity for finite automata.
Functoriality and number of solutions of congruences
Functoriality and the Inverse Galois problem II: groups of type and
This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ? Let be a prime and a positive integer. We show that that the finite simple groups of Lie type if and appear as Galois groups over , for some divisible by . In particular, for each of the two Lie types and fixed we construct infinitely many Galois groups but we do not have a precise control...
Functoriality for the classical groups
Fundamental domains for Shimura curves
We describe a process for defining and computing a fundamental domain in the upper half plane of a Shimura curve associated with an order in a quaternion algebra . A fundamental domain for realizes a finite presentation of the quaternion unit group, modulo units of its center. We give explicit examples of domains for the curves . The first example is a classical example of a triangle group and the second is a corrected version of that appearing in the book of Vignéras [13], due to Michon....
Fundamental groups and Diophantine geometry
This is a brief exposition on the uses of non-commutative fundamental groups in the study of Diophantine problems.