Revisiting Rademacher's formula for the partition function p(n)

被引：7

作者：

Pribitkin, WD ^{[1
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

RAMANUJAN JOURNAL | 2000年 / 4卷 / 04期

关键词：

partitions; modular forms; Fourier coefficients;

D O I：

10.1023/A:1009828302300

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a new proof of Rademacher's celebrated exact formula for the partition function. Along the way we present a simple treatment of an integral which is ubiquitous in the theory of nonanalytic automorphic forms.

引用

页码：455 / 467

页数：13

共 19 条

[1]

[Anonymous], 1989, P S PURE MATH

[2]

Dedekind R., 1877, J REINE ANGEW MATH, V83, P265

[3] KLOOSTERMAN SUMS AND FOURIER COEFFICIENTS OF CUSP FORMS [J].

DESHOUILLERS, JM ;

IWANIEC, H .

INVENTIONES MATHEMATICAE, 1982, 70 (02) :219-288

[4]

Hardy GH, 1918, P LOND MATH SOC, V17, P75

[5]

HECKE E, 1959, MATH WERKE, P461

[6]

Hejhal D.A., 1983, The Selberg trace formula for PSL(2,R), V2, P1001

[7] ON THE FOURIER COEFFICIENTS OF SMALL POSITIVE POWERS OF THETA-(TAU) [J].

KNOPP, MI .

INVENTIONES MATHEMATICAE, 1986, 85 (01) :165-183

[8] PETERSSON CONJECTURE FOR CUSP FORMS OF WEIGHT ZERO AND LINNIK CONJECTURE - SUMS OF KLOOSTERMAN SUMS [J].

KUZNECOV, NV .

MATHEMATICS OF THE USSR-SBORNIK, 1981, 39 (03) :299-342

[9] CONSTRUCTION OF AUTOMORPHIC FORMS AND INTEGRALS [J].

NIEBUR, D .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 191 (464) :373-385

[10]

Pribitkin WD, 2000, ACTA ARITH, V93, P343

← 1 2 →