The divisor function over arithmetic progressions

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Authors ¹, ², ³

Université de Paris-Sud, Mathématique Bât. 425, 91405 Orsay, France
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.
Department of Mathematics, Princeton University, Princeton, New Jersey 08544, U.S.A.

[1] A. Adolphson and S. Sperber, Exponential sums and Newton polyhedra, Bull. Amer. Math. Soc. 16 (1987), 282-286.
[2] A. Adolphson and S. Sperber, Exponential sums on (Gₘ)ⁿ, Invent. Math. 101 (1990), 63-79.
[3] E. Fouvry, Sur le problème des diviseurs de Titchmarsh, J. Reine Angew. Math. 357 (1985), 51-76.
[4] J. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem (with appendix by B. J. Birch and E. Bombieri), Ann. of Math. 121 (1985), 319-350.
[De-Weil II] P. Deligne, La conjecture de Weil II, Publ. Math. I.H.E.S. 52 (1981), 313-428.
[SGA] A. Grothendieck et al., Séminaire de Géométrie Algébrique du Bois- Marie, SGA 1, SGA 4, Parts I, II, and III, SGA 4 1/2, SGA 5, SGA 7, Parts I and II, Lecture Notes in Math. 224, 269-270-305, 569, 589, 288-340, Springer, Berlin 1971 to 1977.
[[Ka-ESDE, 7.4] N. Katz, Exponential Sums and Differential Equations, Ann. of Math. Stud. 124, Princeton Univ. Press, 1990.
[Ka-GKM] N. Katz, Gauss Sums, Kloosterman Sums and Monodromy Groups, Ann. of Math. Stud. 116, Princeton Univ. Press, 1988.
[Ka-Lg] N. Katz, Local to global extensions of representations of fundamental groups, Ann. Inst. Fourier (Grenoble) 36 (4) (1986), 59-106.
[Weil] A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-207.