Non-linear Twists of L-Functions: A Survey

Bochner S.: On Riemann’s functional equation with multiple gamma factors. Ann. of Math. 67, 29–41 (1958)

Carletti E., Monti Bragadin G., Perelli A.: A note on Hecke’s functional equation and the Selberg class. Funct. et Approx. 41, 211–220 (2009)

Conrey J.B., Ghosh A.: On the Selberg class of Dirichlet series: small degrees. Duke Math. J. 72, 673–693 (1993)

R. Hartshorne, Algebric Geometry. Springer Verlag, 1977.

E. Hecke, Lectures on Dirichlet Series, Modular Functions and Quadratic Forms. Vanderhoeck & Ruprecht, 1983.

Jutila M.: Lectures on a Method in the Theory of Exponential Sums. Springer Verlag, Tata Institute of Fundamental Research (1987)

J. Kaczorowski, Axiomatic theory of L-functions: the Selberg class. In Analytic Number Theory, C.I.M.E. Summer School, Cetraro (Italy) 2002, ed. by A.Perelli and C.Viola, 133–209, Springer L.N. 1891, 2006.

Kaczorowski J., Molteni G., Perelli A.: Unique factorization results for semigroups of L-functions. Math. Ann. 341, 517–527 (2008)

Kaczorowski J., Perelli A.: On the structure of the Selberg class, I: 0 ≤ d ≤ 1. Acta Math. 182, 207–241 (1999)

J. Kaczorowski, A. Perelli, The Selberg class: a survey. In Number Theory in Progress, Proc. Conf. in Honor of A.Schinzel, ed. by K.Györy et al., 953–992, de Gruyter, 1999.

Kaczorowski J., Perelli A.: On the structure of the Selberg class, V: 1 ≥ d ≥ 5/3. Invent. Math. 150, 485–516 (2002)

Kaczorowski J., Perelli A.: A remark on solutions of functional equations of Riemann’s type. Funct. et Approx. 32, 51–56 (2004)

Kaczorowski J., Perelli A.: On the structure of the Selberg class, VI: non-linear twists. Acta Arith. 116, 315–341 (2005)

J. Kaczorowski, A. Perelli, On the structure of the Selberg class, VII: 1 < d < 2. To appear in Annals of Math.

J. Kaczorowski, A. Perelli, Zeta functions of finite fields and the Selberg class. In preparation.

J. Kaczorowski, A. Perelli, Introduction to the Selberg Class of L-Functions. In preparation.

H.L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis. A.M.S. Publ., 1994.

Perelli A.: A survey of the Selberg class of L-functions, part I. Milan J. Math. 73, 19–52 (2005)

A. Perelli, A survey of the Selberg class of L-functions, part II, Riv. Mat. Univ. Parma (7) 3* (2004), 83–118.

Richert H.-E.: Über Dirichletreihen mit Funktionalgleichung. Publ. Inst. Math. Acad. Serbe Sci. 11, 73–124 (1957)

A. Selberg, Old and new conjectures and results about a class of Dirichlet series. In Proc. Amalfi Conf. Analytic Number Theory, ed. by E.Bombieri et al., 367–385, Università di Salerno 1992; Collected Papers, vol. II, 47–63, Springer Verlag, 1991.