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1

Ramanujan's Series for 1/π: A Survey

Nayandeep Deka Baruah, Bruce C. Berndt and Heng Huat Chan

Journal:

American Mathematical Monthly

Year:

2009

Language:

english

File:

PDF, 1.51 MB

english, 2009

2

Eisenstein series and Ramanujan-type series for 1/π

Nayandeep Deka Baruah, Bruce C. Berndt

Journal:

The Ramanujan Journal

Year:

2010

Language:

english

File:

PDF, 592 KB

english, 2010

3

Ramanujan's series for arising from his cubic and quartic theories of elliptic functions

Nayandeep Deka Baruah, Bruce C. Berndt

Journal:

Journal of Mathematical Analysis and Applications

Year:

2008

Language:

english

File:

PDF, 165 KB

english, 2008

4

Modular relations for the nonic analogues of the Rogers–Ramanujan functions with applications to partitions

Nayandeep Deka Baruah, Jonali Bora

Journal:

Journal of Number Theory

Year:

2008

Language:

english

File:

PDF, 232 KB

english, 2008

5

On some of Ramanujan's Schläfli-type “mixed” modular equations

Nayandeep Deka Baruah

Journal:

Journal of Number Theory

Year:

2003

Language:

english

File:

PDF, 216 KB

english, 2003

6

Some new proofs of modular relations for

Nayandeep Deka Baruah, Jonali Bora, Nipen Saikia

Journal:

The Ramanujan Journal

Year:

2008

Language:

english

File:

PDF, 432 KB

english, 2008

7

Analogues of Ramanujan’s partition identities and congruences arising from his theta functions and modular equations

Nayandeep Deka Baruah, Kanan Kumari Ojah

Journal:

The Ramanujan Journal

Year:

2012

Language:

english

File:

PDF, 684 KB

english, 2012

8

SOME CONGRUENCES DEDUCIBLE FROM RAMANUJAN'S CUBIC CONTINUED FRACTION

BARUAH, NAYANDEEP DEKA, OJAH, KANAN KUMARI

Journal:

International Journal of Number Theory

Year:

2011

Language:

english

File:

PDF, 238 KB

english, 2011

9

Identities and congruences for the general partition and Ramanujan’s tau functions

Nayandeep Deka Baruah,Bipul Kumar Sarmah

Journal:

Indian Journal of Pure and Applied Mathematics

Year:

2013

File:

PDF, 3.28 MB

2013

10

Colored partition identities conjectured by Sandon and Zanello

Baruah, Nayandeep Deka, Boruah, Bidyut

Journal:

The Ramanujan Journal

Year:

2015

Language:

english

File:

PDF, 450 KB

english, 2015

11

Infinite families of arithmetic identities and congruences for bipartitions with 3-cores

Baruah, Nayandeep Deka, Nath, Kallol

Journal:

Journal of Number Theory

Year:

2015

Language:

english

File:

PDF, 288 KB

english, 2015

12

Parity results for broken 5-diamond, 7-diamond and 11-diamond partitions

Ahmed, Zakir, Baruah, Nayandeep Deka

Journal:

International Journal of Number Theory

Year:

2015

Language:

english

File:

PDF, 279 KB

english, 2015

13

SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS INDUCED BY PARTITIONS OF 8

BARUAH, NAYANDEEP DEKA, COOPER, SHAUN, HIRSCHHORN, MICHAEL

Journal:

International Journal of Number Theory

Year:

2008

Language:

english

File:

PDF, 187 KB

english, 2008

14

INFINITE FAMILIES OF ARITHMETIC IDENTITIES FOR DOUBLED DISTINCT t-CORES FOR t = 3, 4, …, 10

BARUAH, NAYANDEEP DEKA, NATH, KALLOL

Journal:

International Journal of Number Theory

Year:

2014

Language:

english

File:

PDF, 283 KB

english, 2014

15

Congruences modulo p2

Baruah, Nayandeep Deka, Ahmed, Zakir

Journal:

Journal of Number Theory

Year:

2015

Language:

english

File:

PDF, 254 KB

english, 2015

16

IDENTITIES FOR SELF-CONJUGATE 7- AND 9-CORE PARTITIONS

BARUAH, NAYANDEEP DEKA, SARMAH, BIPUL KUMAR

Journal:

International Journal of Number Theory

Year:

2012

Language:

english

File:

PDF, 185 KB

english, 2012

17

INFINITE FAMILIES OF ARITHMETIC IDENTITIES FOR 4-CORES

DEKA BARUAH, NAYANDEEP, NATH, KALLOL

Journal:

Bulletin of the Australian Mathematical Society

Year:

2013

Language:

english

File:

PDF, 148 KB

english, 2013

18

Generalized Frobenius partitions with 6 colors

Baruah, Nayandeep Deka, Sarmah, Bipul Kumar

Journal:

The Ramanujan Journal

Year:

2015

Language:

english

File:

PDF, 263 KB

english, 2015

19

New congruences modulo 5 for the number of 2-color partitions

Ahmed, Zakir, Baruah, Nayandeep Deka, Dastidar, Manosij Ghosh

Journal:

Journal of Number Theory

Year:

2015

Language:

english

File:

PDF, 228 KB

english, 2015

20

New hypergeometric-like series for $1/\pi^{2}$ arising from Ramanujan’s theory of elliptic functions to alternative base 3

Deka Baruah, Nayandeep, Nayak, Narayan

Journal:

Transactions of the American Mathematical Society

Year:

2011

Language:

english

File:

PDF, 466 KB

english, 2011

21

New congruences for Andrews' singular overpartitions

Ahmed, Zakir, Baruah, Nayandeep Deka

Journal:

International Journal of Number Theory

Year:

2015

Language:

english

File:

PDF, 240 KB

english, 2015

22

New congruences for\(\ell \)-regular partitions for\(\ell \in \{5,6,7,49\}\)

Ahmed, Zakir, Baruah, Nayandeep Deka

Journal:

The Ramanujan Journal

Year:

2016

Language:

english

File:

PDF, 486 KB

english, 2016

23

Partition identities arising from Ramanujan’s formulas for multipliers

Baruah, Nayandeep Deka, Boruah, Bidyut

Journal:

The Ramanujan Journal

Year:

2017

Language:

english

File:

PDF, 517 KB

english, 2017

24

Ramanujan's Series for 1/π: A Survey

Baruah, Nayandeep Deka, Berndt, Bruce C., Chan, Heng Huat

Journal:

American Mathematical Monthly

Year:

2009

Language:

english

File:

PDF, 173 KB

english, 2009

25

Ramanujan's Series for 1/π: A Survey

Baruah, Nayandeep Deka, Berndt, Bruce C., Chan, Heng Huat

Journal:

American Mathematical Monthly

Year:

2009

Language:

english

File:

PDF, 382 KB

english, 2009

26

New congruences modulo 2, 4, and 8 for the number of tagged parts over the partitions with designated summands

Baruah, Nayandeep Deka, Kaur, Mandeep

Journal:

The Ramanujan Journal

Year:

2019

Language:

english

File:

PDF, 307 KB

english, 2019

27

Proofs of Some Conjectures of Z. -H. Sun on Relations Between Sums of Squares and Sums of Triangular Numbers

Baruah, Nayandeep Deka, Kaur, Mandeep, Kim, Mingyu, Oh, Byeong-Kweon

Journal:

Indian Journal of Pure and Applied Mathematics

Year:

2020

File:

PDF, 290 KB

2020

28

Modular Equations for Ramanujan's Cubic Continued Fraction

Nayandeep Deka Baruah

Journal:

Journal of Mathematical Analysis and Applications

Year:

2002

Language:

english

File:

PDF, 100 KB

english, 2002

29

Congruences for generalized Frobenius partitions with 4 colors

Nayandeep Deka Baruah, Bipul Kumar Sarmah

Journal:

Discrete Mathematics

Year:

2011

Language:

english

File:

PDF, 250 KB

english, 2011

30

Partition identities and Ramanujan's modular equations

Nayandeep Deka Baruah, Bruce C. Berndt

Journal:

Journal of Combinatorial Theory, Series A

Year:

2007

Language:

english

File:

PDF, 199 KB

english, 2007

31

Some general theorems on the explicit evaluations of Ramanujan's cubic continued fraction

Nayandeep Deka Baruah, Nipen Saikia

Journal:

Journal of Computational and Applied Mathematics

Year:

2003

Language:

english

File:

PDF, 187 KB

english, 2003

32

Explicit evaluations of Ramanujan-Göllnitz-Gordon continued fraction

Nayandeep Deka Baruah, Nipen Saikia

Journal:

Monatshefte für Mathematik

Year:

2008

Language:

english

File:

PDF, 132 KB

english, 2008

33

Partition identities arising from theta function identities

Nayandeep Deka Baruah, Bruce C. Berndt

Journal:

Acta Mathematica Sinica, English Series (Springer)

Year:

2008

Language:

english

File:

PDF, 271 KB

english, 2008

34

Theta function identities associated with Ramanujan’s modular equations of degree 15

Rupam Barman, Nayandeep Deka Baruah

Journal:

Proceedings Mathematical Sciences

Year:

2010

Language:

english

File:

PDF, 181 KB

english, 2010

35

Ramanujan's Eisenstein series and new hypergeometric-like series for

Nayandeep Deka Baruah, Bruce C. Berndt

Journal:

Journal of Approximation Theory

Year:

2009

Language:

english

File:

PDF, 223 KB

english, 2009

36

Ramanujan’s modular equations of degree 5

BARUAH, NAYANDEEP DEKA, BORA, JONALI, OJAH, KANAN KUMARI

Journal:

Proceedings Mathematical Sciences

Year:

2012

Language:

english

File:

PDF, 281 KB

english, 2012

37

Infinite families of arithmetic identities for self-conjugate 5-cores and 7-cores

Baruah, Nayandeep Deka, Nath, Kallol

Journal:

Discrete Mathematics

Year:

2014

Language:

english

File:

PDF, 400 KB

english, 2014

38

Parity results for 7-regular and 23-regular partitions

Baruah, Nayandeep Deka, Das, Kuwali

Journal:

International Journal of Number Theory

Year:

2015

Language:

english

File:

PDF, 223 KB

english, 2015

39

Some results on $3$-cores

Deka Baruah, Nayandeep, Nath, Kallol

Journal:

Proceedings of the American Mathematical Society

Year:

2013

Language:

english

File:

PDF, 164 KB

english, 2013

40

On Exact Generating Functions for the Number of Partitions into Distinct Parts

Baruah, Nayandeep Deka, Begum, Nilufar Mana

Journal:

International Journal of Number Theory

Year:

2018

Language:

english

File:

PDF, 407 KB

english, 2018

41

Modular relations and explicit values of Ramanujan-Selberg continued fractions

Baruah, Nayandeep Deka, Saikia, Nipen

Journal:

International Journal of Mathematics and Mathematical Sciences

Year:

2006

Language:

english

File:

PDF, 1.89 MB

english, 2006

42

Proofs of some conjectures of Chan on Appell–Lerch sums

Baruah, Nayandeep Deka, Begum, Nilufar Mana

Journal:

The Ramanujan Journal

Year:

2019

Language:

english

File:

PDF, 447 KB

english, 2019

43

New congruences modulo 2, 4, and 8 for the number of tagged parts over the partitions with designated summands

Baruah, Nayandeep Deka, Kaur, Mandeep

Journal:

The Ramanujan Journal

Year:

2019

File:

PDF, 307 KB

2019

44

Some theorems on the explicit evaluation of Ramanujan's theta-functions

Baruah, Nayandeep Deka, Bhattacharyya, P.

Journal:

International Journal of Mathematics and Mathematical Sciences

Year:

2004

Language:

english

File:

PDF, 2.22 MB

english, 2004

45

Two Parameters For Ramanujan's Theta-Functions and Their Explicit Values

Baruah, Nayandeep Deka, Saikia, Nipen

Journal:

Rocky Mountain Journal of Mathematics

Year:

2007

File:

PDF, 367 KB

2007

46

Some results on vanishing coefficients in infinite product expansions

Baruah, Nayandeep Deka, Kaur, Mandeep

Journal:

The Ramanujan Journal

Year:

2019

Language:

english

File:

PDF, 275 KB

english, 2019

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