An analytic class number type formula for PSL2(Z) - TIB AV-Portal

An analytic class number type formula for PSL2(Z)

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Institut Fourier

Pippich, Anna von

Formal Metadata

Title

An analytic class number type formula for PSL2(Z)

Title of Series

Summer School 2017 - Arakelov Geometry and diophantine applications

Number of Parts

43

Author

Pippich, Anna von

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/63256 (DOI)

Publisher

Institut Fourier

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Abstract

For any Fuchsian subgroup Γ⊂PSL2(R) of the first kind, Selberg introduced the Selberg zeta function in analogy to the Riemann zeta function using the lengths of simple closed geodesics on Γ∖H instead of prime numbers. In this talk, we report on a formula that determines the special value at s=1 of the derivative of the Selberg zeta function for Γ=PSL2(Z). This formula is obtained as an application of a generalized Riemann-Roch isometry for the trivial sheaf on ¯Γ∖H, equipped with the Poincaré metric. This is joint work with Gerard Freixas.

Series

Summer School 2017 - Arakelov Geometry and diophantine applications33 / 43

1

55:15

Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (Part 1)

2

59:43

Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (Part 4)

3

1:33:45

Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (Part 2)

4

1:31:53

Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (Part 3)

5

1:31:50

Arithmetic Intersection (Part 1)

6

1:10:09

Arithmetic Intersection (Part 2)

7

1:26:13

Arithmetic Intersection (Part 3)

8

1:24:43

Arithmetic Intersection (Part 4)

9

1:02:21

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 1)

10

1:30:57

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 2)

11

1:03:34

Théorème de Hilbert-Samuel arithmétique (Part 2)

12

1:01:34

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 3)

13

1:33:12

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 4)

14

54:53

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 5)

15

1:31:05

Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part 1)

16

1:24:56

Arakelov theory on Shimura varieties (Part 2)

17

1:26:53

Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part 2)

18

1:21:09

Arakelov theory on Shimura varieties (Part 1)

19

1:00:50

Théorème de Hilbert-Samuel arithmétique (Part 1)

20

1:31:06

Automorphic forms and arithmetic intersections (Part 2)

21

46:14

Automorphic forms and arithmetic intersections (Part 3)

22

1:26:47

Minima et pentes des espaces adéliques rigides (Part 1)

23

1:31:00

Minima et pentes des espaces adéliques rigides (Part 2)

24

1:33:49

Some problems of arithmetic origin in complex dynamics and geometry (Part 1)

25

1:30:23

Minima et pentes des espaces adéliques rigides (Part 3)

26

1:00:10

Sieving rational points on algebraic varieties

27

1:32:37

Some problems of arithmetic origin in complex dynamics and geometry (Part 3)

28

1:29:51

Slopes and distribution of points (Part 1)

29

1:02:42

Slopes and distribution of points (Part 2)

30

55:57

Slopes and distribution of points (Part 3)

31

1:28:47

Slopes and distribution of points (Part 4)

32

1:31:01

Some problems of arithmetic origin in complex dynamics and geometry (Part 2)

33

1:01:14

An analytic class number type formula for PSL2(Z)

34

1:04:38

Quantitative aspects of rational points on algebraic varieties (Part 1)

35

1:00:15

On the arithmetic degree of Shimura curves

36

1:02:27

Diophantine approximation and local distribution of rational points

37

1:03:58

Quantitative aspects of rational points on algebraic varieties (Part 2)

38

1:24:44

Quantitative aspects of rational points on algebraic varieties (Part 3)

39

1:29:59

Quantitative aspects of rational points on algebraic varieties (Part 4)

40

1:31:49

Arithmetic Intersection (Part 1)

41

1:10:09

Arithmetic Intersection (Part 2)

42

1:26:13

Arithmetic Intersection (Part 3)

43

1:03:01

Exceptional splitting of reductions of abelian surfaces with real multiplication

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