Ad­vanced Sem­in­ar "Num­ber The­ory and Arith­met­ic­al Stat­ist­ics"

Sum­mer 2025

Location: D 2 314                    Time: 14:00 - 15:30

The seminar will take place regularly on wednesdays from April 9th, 2025.

Pi­chai Vanch­inath­an (VIT Uni­ver­sity), Lin­ear Dis­joint­ness, Re­lativ­ised Cyc­lo­tom­ic Poly­no­mi­als and In­flated G-ex­ten­sions for Num­ber Fields

Location: D2.314
Organizer: Prof. Dr. Jürgen Klüners

Title:  Linear Disjointness, Relativised Cyclotomic Polynomials and Inflated G-extensions for Number Fields

Abstract: There had been many attempts to generalize cyclotomic polynomials by many authors: combinatorialapproach using MOebius Inversion, Number-Theoretic approacj=h by focussing on unitary divisors etc. Our approach  takes the factorization of X^n-1 as the model and defines cyclotomic polynomials relative to an algebraic integer.

The methods (not the results)  used were surprisingly found to solve a classical question (but asked and solved over Q  only in 2004 and forgotten) over number fields. Given an irreducible polynomial over a number field how many of its roots are found in the extension obtained by adjoining a single root.

Finally we show how to find number field extensions  which are poor in automorphisms -- poor in a precise technical manner having a specified inflation index and a specific group as the automorphism group.

This is a joint work with M Krithika.
 

Pi­chai Vanch­inath­an (VIT Uni­ver­sity), Lin­ear Dis­joint­ness, Re­lativ­ised Cyc­lo­tom­ic Poly­no­mi­als and In­flated G-ex­ten­sions for Num­ber Fields

Location: D2.314
Organizer: Prof. Dr. Jürgen Klüners

Title:  Linear Disjointness, Relativised Cyclotomic Polynomials and Inflated G-extensions for Number Fields

Abstract: There had been many attempts to generalize cyclotomic polynomials by many authors: combinatorialapproach using MOebius Inversion, Number-Theoretic approacj=h by focussing on unitary divisors etc. Our approach  takes the factorization of X^n-1 as the model and defines cyclotomic polynomials relative to an algebraic integer.

The methods (not the results)  used were surprisingly found to solve a classical question (but asked and solved over Q  only in 2004 and forgotten) over number fields. Given an irreducible polynomial over a number field how many of its roots are found in the extension obtained by adjoining a single root.

Finally we show how to find number field extensions  which are poor in automorphisms -- poor in a precise technical manner having a specified inflation index and a specific group as the automorphism group.

This is a joint work with M Krithika.
 

Pi­chai Vanch­inath­an (VIT Uni­ver­sity), Lin­ear Dis­joint­ness, Re­lativ­ised Cyc­lo­tom­ic Poly­no­mi­als and In­flated G-ex­ten­sions for Num­ber Fields

Location: D2.314
Organizer: Prof. Dr. Jürgen Klüners

Title:  Linear Disjointness, Relativised Cyclotomic Polynomials and Inflated G-extensions for Number Fields

Abstract: There had been many attempts to generalize cyclotomic polynomials by many authors: combinatorialapproach using MOebius Inversion, Number-Theoretic approacj=h by focussing on unitary divisors etc. Our approach  takes the factorization of X^n-1 as the model and defines cyclotomic polynomials relative to an algebraic integer.

The methods (not the results)  used were surprisingly found to solve a classical question (but asked and solved over Q  only in 2004 and forgotten) over number fields. Given an irreducible polynomial over a number field how many of its roots are found in the extension obtained by adjoining a single root.

Finally we show how to find number field extensions  which are poor in automorphisms -- poor in a precise technical manner having a specified inflation index and a specific group as the automorphism group.

This is a joint work with M Krithika.
 

Pi­chai Vanch­inath­an (VIT Uni­ver­sity), Lin­ear Dis­joint­ness, Re­lativ­ised Cyc­lo­tom­ic Poly­no­mi­als and In­flated G-ex­ten­sions for Num­ber Fields

Location: D2.314
Organizer: Prof. Dr. Jürgen Klüners

Title:  Linear Disjointness, Relativised Cyclotomic Polynomials and Inflated G-extensions for Number Fields

Abstract: There had been many attempts to generalize cyclotomic polynomials by many authors: combinatorialapproach using MOebius Inversion, Number-Theoretic approacj=h by focussing on unitary divisors etc. Our approach  takes the factorization of X^n-1 as the model and defines cyclotomic polynomials relative to an algebraic integer.

The methods (not the results)  used were surprisingly found to solve a classical question (but asked and solved over Q  only in 2004 and forgotten) over number fields. Given an irreducible polynomial over a number field how many of its roots are found in the extension obtained by adjoining a single root.

Finally we show how to find number field extensions  which are poor in automorphisms -- poor in a precise technical manner having a specified inflation index and a specific group as the automorphism group.

This is a joint work with M Krithika.