Modular properties of full 5D SYM partition function
نویسندگان
چکیده
منابع مشابه
The Partition Function and Modular Forms
1. Intro to partition function and modular forms 1 2. Partition function leading term, without modular forms 2 3. Modular form basics 5 4. First application: Rademacher’s formula 6 4.1. A Transformation Formula for the η Function 6 4.2. Rademacher’s Convergent Series 14 5. Second application: Ramanujan congruences 22 5.1. Additional Results from Modular Functions 22 5.2. Proof of Ramanujan Cong...
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Ramanujan’s famous partition congruences modulo powers of 5, 7, and 11 imply that certain sequences of partition generating functions tend `-adically to 0. Although these congruences have inspired research in many directions, little is known about the `-adic behavior of these sequences for primes ` ≥ 13. We show that these sequences are governed by “fractal” behavior. Modulo any power of a prim...
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Eighty years ago, Ramanujan conjectured and proved some striking congruences for the partition function modulo powers of 5, 7, and 11. Until recently, only a handful of further such congruences were known. Here we report that such congruences are much more widespread than was previously known, and we describe the theoretical framework that appears to explain every known Ramanujan-type congruence.
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2016
ISSN: 1029-8479
DOI: 10.1007/jhep03(2016)193