zeta-functions of automorphic forms,
modular forms in several variables,
multiplicative arithmetic of quadratic forms,
Hecke operators,
spherical functions,
theta-functions.
Main publications:
Andrianov A. N., Quadratic forms and Hecke operators, Grundlehren der Math. Wiss., 286, Springer-Verlag, Berlin, 1987, 374 p.
Andrianov A. N., Zhuravlev V. G., Modulyarnye formy i operatory Gekke, Nauka, Moskva, 1990, 447 s.
Andrianov A. N., “Singulyarnye koltsa Gekke–Shimury i operatory Gekke na zigelevykh modulyarnykh formakh”, Algebra i analiz, 11:6 (1999), 1–68
Andrianov A., “On functional equations satisfied by spinor Euler products for Siegel modular forms of genus 2 with characters”, Abh. Math. Sem. Univ. Hamburg, 71 (2001), 123–142
A. Andrianov, “Interaction of Hecke–Shimura rings and zeta functions”, Zap. Nauchn. Sem. POMI, 449 (2016), 5–14; J. Math. Sci. (N. Y.), 225:6 (2017), 841–847
2015
2.
A. N. Andrianov, “Fractional factorials and prime numbers (A remark on the paper “On prime values of some quadratic polynomials”)”, Zap. Nauchn. Sem. POMI, 440 (2015), 5–7; J. Math. Sci. (N. Y.), 217:1 (2016), 1–2
2014
3.
A. N. Andrianov, “On prime values of some quadratic polynomials”, Zap. Nauchn. Sem. POMI, 429 (2014), 5–10; J. Math. Sci. (N. Y.), 207:6 (2015), 803–807
A. Andrianov, “Interaction of Hecke–Shimura rings acting on theta-series”, Zap. Nauchn. Sem. POMI, 418 (2013), 8–27; J. Math. Sci. (N. Y.), 200:5 (2014), 521–531
2012
5.
A. N. Andrianov, “On interaction of symplectic and orthogonal Hecke–Shimura rings of one-class quadratic forms”, Zap. Nauchn. Sem. POMI, 404 (2012), 5–17; J. Math. Sci. (N. Y.), 193:1 (2013), 1–7
2011
6.
A. N. Andrianov, “Zeta-functions of harmonic theta-series and prime numbers”, Algebra i Analiz, 23:2 (2011), 52–76; St. Petersburg Math. J., 23:2 (2012), 239–255
2008
7.
A. Andrianov, “Twisting of Siegel modular forms with characters, and $L$-functions”, Algebra i Analiz, 20:6 (2008), 1–29; St. Petersburg Math. J., 20:6 (2009), 851–871
A. N. Andrianov, “Action of Hecke operators on Maass theta series and zeta functions”, Algebra i Analiz, 19:5 (2007), 3–36; St. Petersburg Math. J., 19:4 (2008), 675–698
A. N. Andrianov, “Zeta functions of orthogonal groups of integral positive-definite quadratic forms”, Uspekhi Mat. Nauk, 61:6(372) (2006), 3–44; Russian Math. Surveys, 61:6 (2006), 999–1038
A. N. Andrianov, “On zeta functions of orthogonal groups of one-class positive definite quadratic forms”, Algebra i Analiz, 17:4 (2005), 3–41; St. Petersburg Math. J., 17:4 (2006), 553–579
A. N. Andrianov, “The action of Hecke operators on theta functions with rational characteristics”, Algebra i Analiz, 15:5 (2003), 109–137; St. Petersburg Math. J., 15:5 (2004), 715–732
2001
12.
A. N. Andrianov, “Around the Ikeda Lift”, Funktsional. Anal. i Prilozhen., 35:2 (2001), 70–74; Funct. Anal. Appl., 35:2 (2001), 138–141
A. N. Andrianov, A. A. Panchishkin, “Singular Frobenius operators on Siegel modular forms with characters, and zeta functions”, Algebra i Analiz, 12:2 (2000), 64–99; St. Petersburg Math. J., 12:2 (2001), 233–257
A. N. Andrianov, “Singular Hecke–Shimura rings and Hecke operators on Siegel modular forms”, Algebra i Analiz, 11:6 (1999), 1–68; St. Petersburg Math. J., 11:6 (2000), 931–987
A. N. Andrianov, “On an advise of Yu. V. Linnik, Hecke operators, and theta functions”, Zap. Nauchn. Sem. POMI, 226 (1996), 5–13; J. Math. Sci. (New York), 89:1 (1998), 909–914
A. N. Andrianov, “Symmetries of harmonic theta-functions of integral quadratic forms”, Uspekhi Mat. Nauk, 50:4(304) (1995), 3–44; Russian Math. Surveys, 50:4 (1995), 661–700
A. N. Andrianov, “Quadratic comparisons and rationality of local zeta series of ternary and quaternary quadratic forms”, Algebra i Analiz, 6:2 (1994), 3–52; St. Petersburg Math. J., 6:2 (1995), 199–240
A. N. Andrianov, “Automorphic factorizations of solutions of quadratic congruences and their applications”, Algebra i Analiz, 5:5 (1993), 1–46; St. Petersburg Math. J., 5:5 (1994), 869–906
A. N. Andrianov, “Multiplicative decompositions of integral representations of binary quadratic forms”, Algebra i Analiz, 5:1 (1993), 81–108; St. Petersburg Math. J., 5:1 (1994), 71–95
A. N. Andrianov, “Multiplicative properties of solutions of quadratic Diophantine problems”, Algebra i Analiz, 2:1 (1990), 3–46; Leningrad Math. J., 2:1 (1991), 1–39
A. N. Andrianov, “On integration of modular forms with theta-series”, Zap. Nauchn. Sem. LOMI, 183 (1990), 5–21; J. Soviet Math., 62:4 (1992), 2833–2844
1989
24.
A. N. Andrianov, “Dirichlet series that correspond to representations of zero by indefinite quadratic forms”, Algebra i Analiz, 1:3 (1989), 71–82; Leningrad Math. J., 1:3 (1990), 635–646
A. N. Andrianov, “Computation of coefficients in transformation formulas of inhomogeneous theta series under the action of Hecke operators”, Zap. Nauchn. Sem. LOMI, 160 (1987), 9–15
A. N. Andrianov, “The action of Hecke operators on nonhomogeneous theta series”, Mat. Sb. (N.S.), 131(173):3(11) (1986), 275–292; Math. USSR-Sb., 59:2 (1988), 269–285
A. N. Andrianov, “Hecke operators and representations of binary quadratic forms”, Trudy Mat. Inst. Steklov., 165 (1984), 4–15; Proc. Steklov Inst. Math., 165 (1985), 3–15
A. N. Andrianov, “Duality in Siegel's theorem on representation by a genus of quadratic forms, and the averaging operator”, Mat. Sb. (N.S.), 122(164):1(9) (1983), 3–11; Math. USSR-Sb., 50:1 (1985), 1–10
A. N. Andrianov, “Degeneration of rings of Hecke operators on spaces of theta-series”, Trudy Mat. Inst. Steklov., 157 (1981), 3–18; Proc. Steklov Inst. Math., 157 (1983), 1–17
A. N. Andrianov, V. L. Kalinin, “On the analytic properties of standard zeta functions of siegel modular forms”, Mat. Sb. (N.S.), 106(148):3(7) (1978), 323–339; Math. USSR-Sb., 35:1 (1979), 1–17
A. N. Andrianov, “Euler expansions of theta-transforms of Siegel modular forms of degree $n$”, Mat. Sb. (N.S.), 105(147):3 (1978), 291–341; Math. USSR-Sb., 34:3 (1978), 259–300
A. N. Andrianov, G. N. Maloletkin, “Behavior of theta-series of genus $n$ of indeterminate quadratic forms under modular substitution”, Trudy Mat. Inst. Steklov., 148 (1978), 5–15; Proc. Steklov Inst. Math., 148 (1980), 1–12
A. N. Andrianov, “On factorization of Hecke polynomials for the sympletic group of genus $n$”, Mat. Sb. (N.S.), 104(146):3(11) (1977), 390–427; Math. USSR-Sb., 33:3 (1977), 343–373
A. N. Andrianov, “On relations between the Hecke rings of groups $\mathrm{Sp}_n$ and $\mathrm{SL}_n$”, Zap. Nauchn. Sem. LOMI, 71 (1977), 5–15; J. Soviet Math., 20:6 (1982), 2501–2509
1976
38.
A. N. Andrianov, “On the zeta-functions of systems of quadratic forms”, Mat. Zametki, 20:1 (1976), 27–34; Math. Notes, 20:1 (1976), 571–574
39.
A. N. Andrianov, “Symmetric squares of zeta-functions of Siegel modular forms of genus 2”, Trudy Mat. Inst. Steklov., 142 (1976), 22–45; Proc. Steklov Inst. Math., 142 (1979), 21–45
A. N. Andrianov, G. N. Maloletkin, “Behavior of theta series of degree $n$ under modular substitutions”, Izv. Akad. Nauk SSSR Ser. Mat., 39:2 (1975), 243–258; Math. USSR-Izv., 9:2 (1975), 227–241
A. N. Andrianov, “Euler products corresponding to Siegel modular froms of genus 2”, Uspekhi Mat. Nauk, 29:3(177) (1974), 43–110; Russian Math. Surveys, 29:3 (1974), 45–116
A. N. Andrianov, O. M. Fomenko, “Distribution of the norms of the hyperbolic elements of the modular group and the class number of indefinite binary quadratic forms”, Dokl. Akad. Nauk SSSR, 196:4 (1971), 743–745
A. N. Andrianov, “Dirichlet series with Euler product in the theory of Siegel modular forms of genus two”, Trudy Mat. Inst. Steklov., 112 (1971), 73–94; Proc. Steklov Inst. Math., 112 (1971), 70–93
A. N. Andrianov, “Spherical functions for $GL_n$ over local fields, and summation of Hecke series”, Mat. Sb. (N.S.), 83(125):3(11) (1970), 429–451; Math. USSR-Sb., 12:3 (1970), 429–452
A. N. Andrianov, “Rationality theorems for Hecke series and zeta functions of the groups $GL_n$ and $Sp_n$ over local fields”, Izv. Akad. Nauk SSSR Ser. Mat., 33:3 (1969), 466–505; Math. USSR-Izv., 3:3 (1969), 439–476
A. N. Andrianov, “Rationality of multiple Hecke series of the full linear group and Shimura's hypothesis on Hecke series of the Symplectic group”, Dokl. Akad. Nauk SSSR, 183:1 (1968), 9–11
A. N. Andrianov, “Continuability and a functional equation for zetafunctions with nonabelian characters of simple algebras over number fields”, Dokl. Akad. Nauk SSSR, 181:4 (1968), 775–777
48.
A. N. Andrianov, “Zeta-functions of simple algebras with non-abelian characters”, Uspekhi Mat. Nauk, 23:4(142) (1968), 3–66; Russian Math. Surveys, 23:4 (1968), 1–65
A. N. Andrianov, “On the representations of the modular group on spaces of parabolic forms”, Dokl. Akad. Nauk SSSR, 165:4 (1965), 735–737
51.
A. N. Andrianov, “The representation of numbers by certain quadratic forms in connection with the theory of elliptic curves”, Izv. Akad. Nauk SSSR Ser. Mat., 29:1 (1965), 227–238
A. N. Andrianov, O. M. Fomenko, “On square means of progressions of Fourier coefficients of parabolic forms”, Trudy Mat. Inst. Steklov., 80 (1965), 5–15; Proc. Steklov Inst. Math., 80 (1965), 3–14
A. N. Andrianov, “The analytic arithmetic of quadratic forms in an odd number of variables in connection with the theory of modular forms”, Dokl. Akad. Nauk SSSR, 145:2 (1962), 241–244
1961
55.
A. N. Andrianov, “Generalization of Eichler's theorem in the theory of quaternary quadratic forms”, Dokl. Akad. Nauk SSSR, 141:1 (1961), 9–12
1994
56.
A. N. Andrianov, A. I. Vinogradov, E. P. Golubeva, G. V. Kuz'mina, A. P. Oskolkov, O. M. Fomenko, “Boris F. Skubenko. An essay on his life and scientific work”, Zap. Nauchn. Sem. POMI, 212 (1994), 5–9; J. Math. Sci., 83:6 (1997), 689–693
A. N. Andrianov, A. I. Vinogradov, Yu. V. Linnik, A. V. Malyshev, D. K. Faddeev, N. G. Chudakov, V. A. Yakubovich, “On book of N. I. Gavrilov, The Riemann problem on the distribution of the roots of the zeta function”, Uspekhi Mat. Nauk, 26:3(159) (1971), 238–247