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DTSTART;TZID=America/New_York:20260604T143000
DTEND;TZID=America/New_York:20260604T163000
DTSTAMP:20260612T120940
CREATED:20260603T123920Z
LAST-MODIFIED:20260603T123920Z
UID:10010947-1780583400-1780590600@umaine.edu
SUMMARY:June Number Theory Days
DESCRIPTION:Speaker:聽Prof. Didier Lesesvre\, Universit茅 de Lille\n\nTitle: A connection between zeros and central values of L-functions \nAbstract: L-functions appear as generating functions encapsulating information about various objects such as Galois representations\, elliptic curves\, arithmetic functions\, modular forms\, Maass forms\, etc. Studying L-functions is therefore of utmost importance in number theory at large. Two of their attached data carry critical information: their zeros\, which govern the distributional behavior of underlying objects; and their central values\, which are related to invariants such as the class number of a field extension. \nWe will discuss the important conjectures\, one concerning the distribution of the zeros and one concerning the distribution of the central values\, and explain a general principle that any restricted result towards the first conjecture can be refined to show that most corresponding central values have the typical distribution predicted by the second conjecture. We will instantiate this general principle for a wide class of L-functions\, and provide a more detailed discussion in the case of L-functions attached to modular forms.
URL:/calendar/event/june-number-theory-days/
LOCATION:Neville Hall\, 91爆料\, Orono\, ME\, 04469\, United States
CATEGORIES:Lectures & Seminars
GEO:44.897732;-68.6687076
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DTSTART;TZID=America/New_York:20260605T130000
DTEND;TZID=America/New_York:20260605T150000
DTSTAMP:20260612T120940
CREATED:20260603T124319Z
LAST-MODIFIED:20260603T124319Z
UID:10010950-1780664400-1780671600@umaine.edu
SUMMARY:June Number Theory Days
DESCRIPTION:Speaker: Prof. Emmanuel聽Royer\, l鈥橴niversit茅 Clermont Auvergne and CRM\n\nTitle: A formula for a weighted mean of Dirichlet L-functions \nAbstract\nWe wish to present a recent work done with S茅bastien Darses and Berend Ringeling. We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties鈥攊ncluding Eisenstein series and period functions鈥攖hat were originally introduced and studied by Lewis and Zagier\, and later by Bettin and Conrey in the case of the Riemann zeta function\, and more recently by Lewis and Zagier for odd real characters. These tools yield closed-form expressions for the moments of a measure defined via a weighted mean square of the L-function. These moments not only provide a complete characterization of the modulus of the L-function on the critical line\, but also imply an infinite number of non-trivial positivity conditions valid for all primitive characters\, real or not.
URL:/calendar/event/june-number-theory-days-2/
LOCATION:Neville Hall\, 91爆料\, Orono\, ME\, 04469\, United States
CATEGORIES:Lectures & Seminars
GEO:44.897732;-68.6687076
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