Related papers: Remarks on an interpolation between Wilson's theor…
The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these…
We develop a framework to investigate conjectures on congruences between the algebraic part of special values of $L$-functions of congruent motives. We show that algebraic local Euler factors satisfy precise interpolation properties in…
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
This note generalizes factorization for formulas with multiplicities and conjectures that the connection method along with this feature is computationally as powerful as resolution, also seen from a complexity point of view.
We briefly summarize the main points made during the discussion session on the determination of $\Delta G/G$, where all Workshop participants were strongly encouraged to contribute.
We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path…
In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…
Dumont has conjectured a marvellous identity, which generalizes, in particular, the classical results of Lagrange, Gauss, Jacobi and Kronecker on the sums of two, three and four squares. We give a combinatorial proof of Dumont's conjecture.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
We present an infinite family of Borwein type $+ - - $ conjectures. The expressions in the conjecture are related to multiple basic hypergeometric series with Macdonald polynomial argument.
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
This is a survey on Sarnak's Conjecture
We generalise a result of D. J. Collins on intersections of conjugates of Magnus subgroups of one-relator groups to the context of one-relator products of locally indicable groups.
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…