Asymptotic Formulas and Generalized Dedekind Sums

REFERENCES

• Almkvist , G. 1993 . “A rather exact formula for the number of plane partitions”. ” . In A tribute to Emil Grosswald: number theory and related analysis Edited by: Knopp , M. and Sheingorn , M. 21 – 26 . Providence , RI : Amer. Math. Soc. . [Almkvist 1993], Contemp. Math. 143
   Google Scholar
• Almkvist , G. 1994 . “Wilf's conjecture and a generalization”. ” . In The Rademacher legacy to mathematics Edited by: Andrews , G. E. 211 – 233 . Providence , RI : Amer. Math. Soc. . [Almkvist 1994], (University Park, PA, 1992), Contemp. Math. 166
   Google Scholar
• Almkvist , G. and Wilf , H. S. 1995 . “On the coefficients in the Hardy-Ramanujan-Rademacher formula for p(n)” . J. Number Theory , 50 ( 2 ) : 329 – 334 . [Almkvist and Wilf 1995]
   Web of Science ®Google Scholar
• Andrews , G. E. 1976 . The theory of partitions, Encyclopedia of Mathematics and its Applications Reading , MA : Addison-Wesley. . [Andrews 1976]
   Google Scholar
• Carlitz , L. and Scoville , R. 1975 . “A generating function for triangular partitions” . Math. Comp. , 29 : 67 – 77 . [Carlitz and Scoville 1975]
   Web of Science ®Google Scholar
• Cheema , M. S. and Conway , W. E. 1972 . “Numerical investigation of certain asymptotic results in the theory of partitions” . Math. Comp. , 26 : 999 – 1005 . [Cheema and Conway 1972], Addendum, 26 (1972), no. 120, loose microfiche suppl. C1–C10
   Web of Science ®Google Scholar
• Dixmier , J. and Nicolas , J.-L. 1990 . “Partitions without small parts”. ” . In Number theory I Edited by: Gy , K. 9 – 33 . Amsterdam : North-Holland. . [Dixmier and Nicolas 1990], (Budapest, 1987), Colloq. Math. Soc. János Bolyai 51
   Google Scholar
• Dokshitzer , T. 1994 . “An elementary proof of Wilf's conjecture”. ” . In The Rademacher legacy to mathematics (University Park, PA, 1992) Edited by: Andrews , G. E. 235 – 243 . Providence , RI : Amer. Math. Soc. . [Dokshitzer 1994], Contemp. Math. 166
   Google Scholar
• Dokshitzer , T. 1995 . “On Wilf's conjecture and generalizations”. ” . In Number theory Edited by: Dilcher , K. 133 – 153 . Providence , RI : Amer. Math. Soc. . [Dokshitzer 1995], (Halifax, Canada, 1994), CMS Conf. Proc. 15
   Google Scholar
• Fee , G. and Granville , A. 1991 . “The prime factors of Wendt's binomial circulant determinant” . Math. Comp. , 57 ( 196 ) : 839 – 848 . [Fee and Granville 1991]
   Web of Science ®Google Scholar
• Garvan , F. G. 1993 . “Some congruences for partitions that are p-cores” . Proc. London Math. Soc. (3) , 66 ( 3 ) : 449 – 478 . [Garvan 1993]
   Google Scholar
• Henrici , P. 1974 . Applied and computational complex analysis, 1: Power series, integration, conformal mapping, location of zeros New York : Wiley-Interscience. . [Henrici 1974]
   Google Scholar
• Kinkelin , J. 1860 . “Über eine mit der Gammafunktion verwandte Transcendente und deren Anwendung auf die Integralrechnung” . J. Reine und Angew. Math , 57 : 122 – 158 . [Kinkelin 1860]
   Google Scholar
• Knessl , C. 1990 . “Asymptotic behaviour of high order differences of the plane partition function” Chicago : Univ. of Illinois. . [Knessl 1990], Preprint
   Google Scholar
• Mellin , H. 1923 . Anwendung einer allgemeinen Methode zur Herleitung asymptotisher Formeln Helsinki : Suomalaisen Tiedeakatemian. . [Mellin 1923]
   Google Scholar
• Milnor , J. 1983 . “On polylogarithms, Hurwitz zeta functions, and the Kubert identities” . Enseign. Math. (2) , 29 ( 3–4 ) : 281 – 322 . [Milnor 1983]
   Google Scholar
• Rademacher , H. 1933 . “Egy reciprocitásképletről a modelfüggvények elméletéből” . Math. Fiz. Lapok , 40 : 24 – 34 . [Rademacher 1933]
   Google Scholar
• Rademacher , H. and Grosswald , E. 1972 . Dedekind sums Washington , DC : The Mathematical Association of America. . [Rademacher and Grosswald 1972], Carus Mathematical Monographs 16
   Google Scholar
• Serre , J.-P. 1977 . Cours d'arithmétique, , 2nd ed. Paris : Presses Universitaires de France. . [Serre 1977], First edition translated as A course in Arithmetic, Springer, 1973
   Google Scholar
• Vardi , I. 1988 . “Determinants of Laplacians and multiple gamma functions” . SIAM J. Math. Anal. , 19 ( 2 ) : 493 – 507 . [Vardi 1988]
   Web of Science ®Google Scholar
• Wright , E. M. 1931 . “Asymptotic partition formulæ, I: Plane partitions” . Quart. J. Math. , 2 : 177 – 189 . [Wright 1931]
   Google Scholar
• Zagier , D. 1986 . “Hyperbolic manifolds and special values of Dedekind zeta-functions” . Invent. Math. , 83 ( 2 ) : 285 – 301 . [Zagier 1986]
   Web of Science ®Google Scholar
• Zucker , I. J. and Robertson , M. M. 1975 . “Exact values for some two-dimensional lattice sums” . J. Phys. A , 8 : 874 – 881 . [Zucker and Robertson 1975]
   Google Scholar