4,080 research outputs found
Zeta-like Multizeta Values for higher genus curves
We prove or conjecture several relations between the multizeta values for
positive genus function fields of class number one, focusing on the zeta-like
values, namely those whose ratio with the zeta value of the same weight is
rational (or conjecturally equivalently algebraic). These are the first known
relations between multizetas, which are not with prime field coefficients. We
seem to have one universal family. We also find that interestingly the
mechanism with which the relations work is quite different from the rational
function field case, raising interesting questions about the expected motivic
interpretation in higher genus. We provide some data in support of the guesses.Comment: Expository revisions plus appendices containing proofs of more cases
of conjecture
A Fast Eigen Solution for Homogeneous Quadratic Minimization with at most Three Constraints
We propose an eigenvalue based technique to solve the Homogeneous Quadratic
Constrained Quadratic Programming problem (HQCQP) with at most 3 constraints
which arise in many signal processing problems. Semi-Definite Relaxation (SDR)
is the only known approach and is computationally intensive. We study the
performance of the proposed fast eigen approach through simulations in the
context of MIMO relays and show that the solution converges to the solution
obtained using the SDR approach with significant reduction in complexity.Comment: 15 pages, The same content without appendices is accepted and is to
be published in IEEE Signal Processing Letter
Diophantine approximation and deformation
We associate certain curves over function fields to given algebraic power
series and show that bounds on the rank of Kodaira-Spencer map of this curves
imply bounds on the exponents of the power series, with more generic curves
giving lower exponents. If we transport Vojta's conjecture on height inequality
to finite characteristic by modifying it by adding suitable deformation
theoretic condition, then we see that the numbers giving rise to general curves
approach Roth's bound. We also prove a hierarchy of exponent bounds for
approximation by algebraic quantities of bounded degree
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