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Does anyone have access to the 1984 dissertation of Franciscus Jozef van der Linden under Hendrik Lenstra? It is called Euclidean Rings with two infinite primes. The theory is that this has the details on Lenstra's three non-principal norm-Euclidean classes for real quadratic fields. In case it is a matter of copying a few pages, apparently the discussion takes place in Section 5.5; this is according to the 2012 dissertation of Pierre Lezowski: and

Note that I have written to both Pierre Lezowski and Hendrik Lenstra, and something may come of that in time. On the other hand, sometimes email gets shunted to spam folders, or people lack adequate time to reply.

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See also:

"The Defenestration of Ermintrude Inch"

"The Love Song of J. Alfred Prufrock"

"The Prime of Miss Jean Brodie"

"The Picture of Dorian Gray"

"The Injudicious Prayers of Pombo the Idolater"

"The Coronation of Mr Thomas Shap"

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I found the thesis (a hard copy, no digital version available) in the catalogue of the library of the University of Amsterdam ( I won't be in town for the coming week, but if you haven't found another version by then it would be no problem to send you a scan. – Philip van Reeuwijk Oct 17 '13 at 23:23
I don't know why, or what it says about me, but I read the second title at the end as "The Love Song of Ben Affleck". – Asaf Karagila Oct 17 '13 at 23:42
Is the prime of Miss Jean Brodie congruent to 1 modulo 4? – Gerry Myerson Oct 18 '13 at 0:47
@GerryMyerson, yes, 57, same as Grothendieck – Will Jagy Oct 18 '13 at 1:15
@S.Carnahan, I noticed that, and that you rejected the suggestion. Thank you. I'll think about it. I am aware that not everyone shares my sense of humor. At the same time, I prefer to know who it is, if someone wishes to alter my writing. I regard the story/book titles as pretty harmless. Well, off to bed. – Will Jagy Oct 18 '13 at 6:15
up vote 9 down vote accepted

The thesis can be found in full here.

Section 5.5 begins on pdf 84/216 (p. 72).

FYI: Because the thesis was published through Centrum voor Wiskunde en Informatica, you can simply search for it through their website:

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Thank you, Benjamin. This is very nice. – Will Jagy Oct 19 '13 at 18:54
You're welcome! Hope you find what you seek. – Benjamin Dickman Oct 20 '13 at 1:53
It's pretty good. It does not give the explicit values desired, but gives methods that should lead to estimates. – Will Jagy Oct 20 '13 at 2:25

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