S. Vlǎduţ

Serge G. Vlǎduţ

Serge G. Vlǎduţ—our dear friend and a member of our editorial board, a prominent specialist in algebraic geometry, number theory, coding theory, and history of mathematics—celebrates his 50th birthday this year.

His research mostly concerns the links of algebraic curves and number fields to other areas of mathematics. In coding theory his name bear two well known asymptotic bounds for code parameters, several bounds for codes with polynomial complexity of construction, basic decoding algorithm for algebraic-geometric codes. In algebraic geometry, everyone knows the Drinfeld–Vlǎduţ theorem on the ratio between the number of points on a curve over a finite field and its genus. He provided the first counter-example to the Gauss class number problem for function fields. He is one of the authors of the fastest algorithm of multiplication in finite fields, based on curves with many points. He obtained very interesting statistics for elliptic curves and abelian varieties over a finite field. Two voluminous books on algebraic geometry codes sum up his results.

His deepest work concerns asymptotic behaviour of class numbers in towers of number fields and algebraic curves, as well as asymptotic properties of zeta-functions. Among the results obtained there is the generalization of the famous Brauer–Siegel theorem establishing the asymptotic behaviour of class numbers of algebraic number fields. Moreover, the statement of the usual Brauer–Siegel theorem is not generally true for towers of number fields, as shown by counter-examples of this paper.

Quite apart stands his work concerning the history of complex multiplication. His book Kronecker Jugendtraum and Modular Functions is a rare example of a history-of-mathematics book on a very advanced topic, that can be written only by a working specialist in the field. That is why the book is read not only by those interested in history, but also by researchers interested in the modern state of the art.

Mathematics is by far not the only interest of his life. High culture, broad education, and deep thought make his discourse extremely interesting, whatever the subject is. His most agreeable personality, warm character, and reliability make him a precious friend and colleague.

We wish Serge to further enrich us with marvelous math and profoundest non-math. Many happy returns of the day!

B. Feigin, Yu. Ilyashenko, Yu. Manin, S. Shlosman, M. Tsfasman

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