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Cover Page The handle http://hdl.handle.net/1887/67539 holds various files of this Leiden University dissertation. Author: Pagano, C. Title: Enumerative arithmetic Issue Date: 2018-12-05

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Cover Page

The handle

http://hdl.handle.net/1887/67539

holds various files of this Leiden University

dissertation.

Author: Pagano, C.

(2)

Enumerative arithmetic

Proefschrift ter verkrijging van

de graad van Doctor aan de Universiteit Leiden op gezag van Rector Magnificus prof. mr. C.J.J.M. Stolker,

volgens besluit van het College voor Promoties te verdedigen op woensdag 5 december 2018

klokke 16:15 uur

door

Carlo Pagano

geboren te Napoli, Itali¨e in 1990

(3)

Promotor: Prof. dr. Hendrik Lenstra

Samenstelling van de promotiecommissie: Prof. dr. Aad van der Vaart (Universiteit Leiden) Prof. dr. Bart de Smit (Universiteit Leiden) Prof. dr. Tim Dokchitser (University of Bristol)

Prof. dr. Felipe Voloch (University of Canterbury, New Zealand) Prof. dr. Melanie Matchett Wood (University of Wisconsin, USA)

Table of content

Chapter 1 On the equation X1 + X2 = 1 in finitely generated

groups in positive characteristic ...5

Addendum to Chapter 1 ...19

Chapter 2 4-Ranks and the general model for statistics of ray class groups of imaginary quadratic number fields ...23

Chapter 3 Jump sets in local fields ...67

(4)

Promotor: Prof. dr. Hendrik Lenstra

Samenstelling van de promotiecommissie: Prof. dr. Aad van der Vaart (Universiteit Leiden) Prof. dr. Bart de Smit (Universiteit Leiden) Prof. dr. Tim Dokchitser (University of Bristol)

Prof. dr. Felipe Voloch (University of Canterbury, New Zealand) Prof. dr. Melanie Matchett Wood (University of Wisconsin, USA)

Table of content

Chapter 1 On the equation X1 + X2 = 1 in finitely generated

groups in positive characteristic ...5

Addendum to Chapter 1 ...19

Chapter 2 4-Ranks and the general model for statistics of ray class groups of imaginary quadratic number fields ...23

Chapter 3 Jump sets in local fields ...67

(5)

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