Abstract:
We obtain an asymptotic formula for the average number of divisors of the quadratic form A(x,y,z)=xy+xz+yzA(x,y,z)=xy+xz+yz, where xx, yy, and zz run through prime numbers from the interval X<x,y,z⩽2X.
Citation:
M. A. Korolev, “Divisors of a quadratic form with primes”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 169–185; Proc. Steklov Inst. Math., 303 (2018), 154–170
\Bibitem{Kor18}
\by M.~A.~Korolev
\paper Divisors of a quadratic form with primes
\inbook Harmonic analysis, approximation theory, and number theory
\bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 303
\pages 169--185
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3949}
\crossref{https://doi.org/10.1134/S0371968518040131}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2018
\vol 303
\pages 154--170
\crossref{https://doi.org/10.1134/S0081543818080138}
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This publication is cited in the following 4 articles:
M. A. Korolev, “Kloosterman Sums with Primes and Solvability of a Congruence with Inverse Residues”, Proc. Steklov Inst. Math., 314 (2021), 96–126
M. A. Korolev, “Kloosterman sums with primes and the solvability of one congruence with inverse residues — II”, Chebyshevskii sb., 21:1 (2020), 221–232
M. A. Korolev, “Kloosterman sums over primes of composite moduli”, Res. Number Theory, 6:2 (2020), 24
M. A. Korolev, “Short Kloosterman Sums with Primes”, Math. Notes, 106:1 (2019), 89–97
Citation in format AMSBIB
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