On Epstein's zeta function and related results in the geometry of numbers
Introductory Workshop: Analytic Number Theory February 06, 2017 - February 10, 2017
Location: SLMath: Eisenbud Auditorium
Epstein zeta function
random lattice
geometry of numbers
11F55 - Other groups and their modular and automorphic forms (several variables)
11R60 - Cyclotomic function fields (class groups, Bernoulli objects, etc.)
11J89 - Transcendence theory of elliptic and abelian functions
On Epstein's Zeta Function And Related Results In The Geometry Of Numbers
In this talk I will discuss certain questions concerning the asymptotic behavior of the Epstein zeta function E_n(L,s) in the limit of large dimension n. In particular I will describe the value distribution of E_n(L,s) for a random lattice L of large dimension n, giving partial answers to questions raised by Sarnak and Strömbergsson in their study of the minima of E_n(L,s). Many of the key ingredients in our discussion will come from the rich interplay between the value distribution of the Epstein zeta function and classical problems in the geometry of numbers
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Sodergren Notes
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On Epstein's Zeta Function And Related Results In The Geometry Of Numbers
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13-Sodergren.mp4
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