ANALYTIC AND COMBINATORIAL NUMBER THEORY: LEGACY RAMANUJAN

This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6–9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday. Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference. Contents: A Triple Integral Analog of a Multiple Zeta Value (T Amdeberhan, V H Moll, A Straub and C Vignat) The Ramanujan–Dyson Identities and George Beck's Congruence Conjectures (G E Andrews) On Entry II.16.12: A Continued Fraction of Ramanujan (G Bhatnagar and M E H Ismail) General Fine Transformations I (D Bowman and S Wesley) Combinatorics of Two Second-Order Mock Theta Functions (H Burson) Chasing After Cancellations: Revisiting a Classic Identity That Implies the Rogers–Ramanujan Identities (H-C Chan) A Mock Theta Function Identity Related to the Partition Rank Modulo 3 and 9 (S H Chan, N Hong, Jerry and J Lovejoy) The Congruence Equation ā + b ≡ c (mod p) (T H Chan) Weighted Partition Rank and Crank Moments I Andrews–Beck Type Congruences (S Chern) Hankel Determinants of Linear Combinations of Moments of Orthogonal Polynomials (J Cigler and C Krattenthaler) Polynomial Analogues of Restricted Multicolor b-ary Partition Functions (K Dilcher and L Ericksen) On Hurwitz Zeta Function and Lommel Functions (A Dixit and R Kumar) An Inequality Between Finite Analogues of Rank and Crank Moments (P Eyyunni, B Maji and G Sood) Asymptotic Expansions, Partial Theta Functions, and Radial Limit Differences of Mock Modular and Modular Forms (A Folsom) On Conjectures of Koike and Somos for Modular identities for the Rogers–Ramanujan Functions (C Gugg) Proof of a Rational Ramanujan-Type Series for 1/𝜋 The Fastest One in Level 3 (J Guillera) Poles of Triple Product L-Functions Involving Monomial Representations (H Hahn) Polynomials and Reciprocals of Eisenstein Series (B Heim and M Neuhauser) Arithmetic Properties of Septic Partition Functions (T Huber, M Huerta and N Mayes) A Twisted Generalization of the Classical Dedekind Sum (B Isaacson) Stability of Asai Local Factors for GL(2) (Y Jo and M Krishnamurthy) Local Densities of Diagonal Integral Ternary Quadratic Forms at Odd Primes (E Jones) Divisibility Properties of the Fourier Coefficients of (Mock) Modular Functions and Ramanujani (S-Y Kang) Restricted k-Color Partitions, II (W J Keith) On Weighted Overpartitions Related to Some q-Series in Ramanujan's Lost Notebook (B Kim, E Kim and J Lovejoy) Twin Nicomachean q-Identities and Conjectures for the Associated Discriminants, Polynomials, and Inequalities (S-H Kim and K B Stolarsky) A Combinatorial Proof of a Recurrence Relation for the Sum of Divisors Function (S Kim) (k, ℓ)-Regular Partitions (L W Kolitsch) A Combinatorial Construction for Two Formulas in Slater's List (K Kurşungöz) Some Observations on Lambert Series, Vanishing Coefficients and Dissections of Infinite Products and Series (J Mc Laughlin) On the Sum of Parts with Multiplicity at Least 2 in All the Partitions of n (M Merca and A J Yee) Mock Modular Eisenstein Series with Nebentypus (M H Mertens, K Ono and L Rolen) The Largest Size of an (s, s + 1)-Core Partition with Parts of the Same Parity (H Nam and M Yu) Holonomic Relations for Modular Functions and Forms: First Guess, then Prove (P Paule and C-S Radu) Equal Sums of Two Cubes of Quadratic Forms (B Reznick)...