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5 papers · 2 filters
Counting lattice points and o-minimal structures
Fabrizio Barroero, Martin Widmer
Let be a lattice in , and let be a definable family in an o-minimal structure over . We give sharp estimates for the number of lattice points in…
Analysis of the Width-w Non-Adjacent Form in Conjunction with Hyperelliptic Curve Cryptography and with Lattices
Daniel Krenn
We analyse the number of occurrences of a fixed non-zero digit in the width-w non-adjacent forms of all elements of a lattice in some region (e.g. a ball). Our result is an asympto…
On Gaps Between Primitive Roots in the Hamming Metric
Rainer Dietmann, Christian Elsholtz, Igor E. Shparlinski
We consider a modification of the classical number theoretic question about the gaps between consecutive primitive roots modulo a prime , which by the well-known result of Burge…
On certain infinite extensions of the rationals with Northcott property
Martin Widmer
A set of algebraic numbers has the Northcott property if each of its subsets of bounded Weil height is finite. Northcott's Theorem, which has many Diophantine applications, states…
On number fields with nontrivial subfields
Martin Widmer
What is the probability for a number field of composite degree to have a nontrivial subfield? As the reader might expect the answer heavily depends on the interpretation of pro…