Includes bibliographical references.

"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."-- Publisher's website.

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 a + b triple bar 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/pi 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) -- Log-concavity results for a biparametric and an elliptic extension of the q-binomial coefficients (M J Schlosser, K Senapati and A K Uncu) -- Analysis and combinatorics of partition Zeta functions (R Schneider and A V Sills) -- Automatic discovery of irrationality proofs and irrationality measures (D Zeilberger and W Zudilin).

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