"Distribution of sums of squares in arithmetic progressions"
by Akshay Ashok Puri
The main goal of this thesis is to obtain an asymptotic formula forn =x21+x22 =x23+x24 x withn⌘a(modq),(a, q) = 1,x4 is a prime andx! 1. This generalizes the work of Daniel and the advisor to the case of arithmetic progressions.
The implemented tools include basic sieve technology, various estimates for the error term in prime number theorem in arithmetic progressions as well as rather standard applications of Hensel’s lemma.
Note that due to the nature of the sequences in question the celebrated Bombieri-Vinogradov theorem can nit be successfully applied here, thus one has to deal rather carefully with the remainder terms at each step, which is, indeed, the main feature of such asymptotics.
In my opinion the thesis deserves a good grade, and its author deserves a master’s degree in mathematics.
Работа достойна оценки хорошо,а её автор заслуживает присвоения степени магистра.
With my best regards, Alisa Sedunova, Associate Professor,
Saint Petersburg State University
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