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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Arunabha Biswas''' | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Arunabha Biswas''' | ||
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| bgcolor="#BCD2EE" align="center" | | | bgcolor="#BCD2EE" align="center" | Limiting values of higher Mahler Measure and cyclotomic polynomials. | ||
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| bgcolor="#BCD2EE" | | | bgcolor="#BCD2EE" | We consider the k-higher Mahler measure m_k(P) of a Laurent polynomial P as the integral of log^k |P| over the complex unit circle. In number theory, Lehmer's conjecture and the appearance of higher Mahler measures in L-functions are the main sources of motivation for studying various properties of m_k(P). Beyond number theory, Mahler measure has connections with topological entropies of dynamical systems and polynomial knot invariants. In this talk I shall present (1) an explicit formula for the value of |m_k(P)|/k! as k approaches infinity, (2) some asymptotic results regarding m_k(P) and (3) a scheme to approximate special values of a class of L-functions. | ||
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Revision as of 17:30, 31 August 2016
Return to NTS Spring 2016
Sep 8
| Arunabha Biswas |
| Limiting values of higher Mahler Measure and cyclotomic polynomials. |
| We consider the k-higher Mahler measure m_k(P) of a Laurent polynomial P as the integral of log^k |P| over the complex unit circle. In number theory, Lehmer's conjecture and the appearance of higher Mahler measures in L-functions are the main sources of motivation for studying various properties of m_k(P). Beyond number theory, Mahler measure has connections with topological entropies of dynamical systems and polynomial knot invariants. In this talk I shall present (1) an explicit formula for the value of |m_k(P)|/k! as k approaches infinity, (2) some asymptotic results regarding m_k(P) and (3) a scheme to approximate special values of a class of L-functions. |
Sep 15
Sep 22
| Alex Smith |
| title coming soon |
| abstract coming soon |
Sep 29
| Steve Lester |
| title coming soon |
| abstract coming soon |
Oct 6
| Nicole Looper |
| title coming soon |
| abstract coming soon |
Oct 13
| Ling Long |
| title coming soon |
| abstract coming soon |
Oct 20
| Jack Klys |
| title coming soon |
| abstract coming soon |
Oct 27
| William Duke |
Nov 3
Nov 10
Nov 17
Dec 1
Dec 8
Dec 15
| Efrat Bank |
| Primes in short intervals on curves over finite fields |
| abstract coming soon
|