Atypical averages of root numbers of families of elliptic curves
Christophe Delaunay
(Université Franche-Comté)
This is a work in progress with Chantal David and Sandro Bettin. Is it possible to find families of elliptic curve such that the parity of the rank over Q(t) does not match with the parity of the rank over Q of the specialization? This will be the central question of the talk. We will clarify a little bit the question and then we will explain how we can find such families. Finally, we will study an explicit example that will allow us to exhibit some atypical situations.
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Kloosterman sums and shifted character sums with multiplicative coefficients
Chaohua Jia
(Chinese Academy of Science)
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Limiting values of Lambert series and the secant
zeta-function
Shigeru Kanemitsu
(Kinki University, Fukoka)
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Hardy-Littlewood numbers and Bessel's functions
Alessandro Languasco
(Università di Padova)
We describe a joint result with A. Zaccagnini about an explicit formula involving
non-trivial zeros of the Riemann zeta-function
for the Cesàro averaged number of representations
of a non-square integer as a sum of a prime and a square.
We'll see that Bessel's functions of complex order and real argument
play a role in such an explicit formula.
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Decomposition in infinite extensions of number fields
Christian Maire
(Université Franche-Comté)
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TBA
Leo Murata
(Meijin Gakuin University, Tokyo)
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Some recent results on Diophantine equations
Michel Waldschmidt
(Université Pierre et Marie Curie)
In a series of recent joint papers with Claude Levesque, we produce new families of Diophantine
equations for which effective methods can be applied. We present a survey of this work.
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Prime numbers in short intervals: the Selberg integral and its
generalisations
Alessandro Zaccagnini
(Università di Parma)
We give a summary of recent work with Alessandro Languasco and
Alberto Perelli on the distribution of primes in short intervals, and
describe a variant of the classical Selberg integral that we introduced,
as well as its connections with a more general version of Montgomery's
pair-correlation Conjecture.
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